<PAGE>   1
                                                                   EXHIBIT 10.12

                         ELEVENTH AMENDMENT TO THE THIRD
                        AMENDED AND RESTATED AGREEMENT OF
                  LIMITED PARTNERSHIP OF AIMCO PROPERTIES, L.P.

         This ELEVENTH AMENDMENT TO THE THIRD AMENDED AND RESTATED AGREEMENT OF
LIMITED PARTNERSHIP OF AIMCO PROPERTIES, L.P., dated as of January 13, 2000
(this "Amendment"), is being executed by AIMCO-GP, Inc., a Delaware corporation
(the "General Partner"), as the general partner of AIMCO Properties, L.P., a
Delaware limited partnership (the "Partnership"), pursuant to the authority
conferred on the General Partner by Section 7.3.C(7) of the Third Amended and
Restated Agreement of Limited Partnership of AIMCO Properties, L.P., dated as of
July 29, 1994 (the "Agreement"). Capitalized terms used, but not otherwise
defined herein, shall have the respective meanings ascribed thereto in the
Agreement.

         WHEREAS, on January 11, 2000, the Previous General Partner filed
Articles Supplementary amending its Charter to reclassify 1,816,216 shares of
authorized but unissued shares of its Class A Common Stock, par value $.01 per
share, as shares of its Class M Convertible Cumulative Preferred Stock, par
value $.01 per share (the "Class M Preferred Stock");

         WHEREAS, in accordance with Section 4.3.E of the Agreement, upon the
issuance of any such shares of Class M Preferred Stock, the Previous General
Partner will contribute the net cash proceeds from such issuance to the Special
Limited Partner, which will contribute such net cash proceeds to the Partnership
in exchange for a number of Partnership Preferred Units equal to the number of
shares of Class M Preferred Stock so issued, which Partnership Preferred Units
shall have designations, preferences and other rights, terms and provisions that
are substantially the same as the designations, preferences and other rights,
terms and provisions of the Class M Preferred Stock, except as otherwise set
forth herein; and

         WHEREAS, pursuant to Section 4.2.A of the Agreement, the General
Partner is authorized to determine the designations, preferences and relative,
participating, optional or other special rights, powers and duties of such
Partnership Preferred Units.

         NOW, THEREFORE, in consideration of the foregoing, and other good and
valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, the parties hereto agree as follows:

         1. The Agreement is hereby amended by the addition of a new exhibit,
entitled "Exhibit W," in the form attached hereto, which shall be attached to
and made a part of the Agreement.

         2. Except as specifically amended hereby, the terms, covenants,
provisions and conditions of the Agreement shall remain unmodified and continue
in full force and effect and, except as amended hereby, all of the terms,
covenants, provisions and conditions of the Agreement are hereby ratified and
confirmed in all respects.



<PAGE>   2



         IN WITNESS WHEREOF, this Amendment has been executed as of the date
first written above.

                                       GENERAL PARTNER:

                                       AIMCO-GP, INC.



                                       By: /s/ PETER K. KOMPANIEZ
                                          --------------------------------------
                                          Name: Peter K. Kompaniez
                                          Title:   President and Vice Chairman




                                        2

<PAGE>   3



                                    EXHIBIT W

                       PARTNERSHIP UNIT DESIGNATION OF THE
                       CLASS M PARTNERSHIP PREFERRED UNITS
                            OF AIMCO PROPERTIES, L.P.


         1.       NUMBER OF UNITS AND DESIGNATION.

         A class of Partnership Preferred Units is hereby designated as "Class M
Partnership Preferred Units," and the number of Partnership Preferred Units
constituting such class shall be 1,816,216.

         2.       DEFINITIONS.

         For purposes of the Class M Partnership Preferred Units, the following
terms shall have the meanings indicated in this Section 2, and capitalized terms
used and not otherwise defined herein shall have the meanings assigned thereto
in the Agreement:

         "Agreement" shall mean the Third Amended and Restated Agreement of
         Limited Partnership of the Partnership, dated as of July 29, 1994, as
         amended.

         "Call Date" shall have the meaning set forth in paragraph (a) of
         Section 5 of this Exhibit W.

         "Class M Partnership Preferred Unit" means a Partnership Preferred Unit
         with the designations, preferences and relative, participating,
         optional or other special rights, powers and duties as are set forth in
         this Exhibit W. It is the intention of the General Partner that each
         Class M Partnership Preferred Unit shall be substantially the economic
         equivalent of one share of Class M Preferred Stock.

         "Class M Preferred Stock" means the Class M Convertible Cumulative
         Preferred Stock, par value $0.01 per share, of the Previous General
         Partner.

         "Code" shall mean the Internal Revenue Code of 1986, as amended from
         time to time, or any successor statute thereto. Reference to any
         provision of the Code shall mean such provision as in effect from time
         to time, as the same may be amended, and any successor thereto, as
         interpreted by any applicable regulations or other administrative
         pronouncements as in effect from time to time.

         "Common Stock" shall mean the Class A Common Stock, $.01 par value per
         share, of the Previous General Partner or such shares of the Previous
         General Partner's capital stock into which outstanding shares of Common
         Stock shall be reclassified.



                                       W-1

<PAGE>   4



         "Distribution Payment Date" shall mean any date on which cash dividends
         are paid on all outstanding shares of the Class M Preferred Stock.

         "Junior Partnership Units" shall have the meaning set forth in
         paragraph (c) of Section 8 of this Exhibit W.

         "Parity Partnership Units" shall have the meaning set forth in
         paragraph (b) of Section 8 of this Exhibit W.

          "Partnership" shall mean AIMCO Properties, L.P., a Delaware limited
          partnership.

         "Senior Partnership Units" shall have the meaning set forth in
         paragraph (a) of Section 8 of this Exhibit W.

         3.       DISTRIBUTIONS.

                  On every Distribution Payment Date, the holders of Class M
Partnership Preferred Units shall be entitled to receive distributions payable
in cash in an amount per Class M Partnership Preferred Unit equal to the per
share dividend payable on the Class M Preferred Stock on such Distribution
Payment Date. Each such distribution shall be payable to the holders of record
of the Class M Partnership Preferred Units, as they appear on the records of the
Partnership at the close of business on the record date for the dividend payable
with respect to the Class M Preferred Stock on such Distribution Payment Date.
Holders of Class M Partnership Preferred Units shall not be entitled to any
distributions on the Class M Partnership Preferred Units, whether payable in
cash, property or stock, except as provided herein.

         4.       LIQUIDATION PREFERENCE.

                  (a) In the event of any liquidation, dissolution or winding up
of the Partnership, whether voluntary or involuntary, before any payment or
distribution of the Partnership (whether capital, surplus or otherwise) shall be
made to or set apart for the holders of Junior Partnership Units, the holders of
Class M Partnership Preferred Units shall be entitled to receive the greater of
(i) Twenty-Five Dollars ($25) per Class M Partnership Preferred Unit (the
"Liquidation Preference"), plus an amount per Class M Partnership Preferred Unit
equal to all dividends (whether or not declared or earned) accumulated, accrued
and unpaid on one share of Class M Preferred Stock to the date of final
distribution to such holders, or (ii) the amount that would be payable to the
holders of Partnership Common Units if they had converted all outstanding shares
of Class M Partnership Preferred Units into shares of Partnership Common Units
immediately prior to such liquidation, dissolution or winding up; but such
holders shall not be entitled to any further payment. Until the holders of the
Class M Partnership Preferred Units have been paid the Liquidation Preference in
full, plus an amount equal to all dividends (whether or not declared or earned)
accumulated, accrued and unpaid on the Class M Preferred Stock to the date of
final distribution to such holders, no payment shall be made to any holder of
Junior Partnership Units upon the liquidation, dissolution or winding

                                       W-2

<PAGE>   5



up of the Partnership. If, upon any liquidation, dissolution or winding up of
the Partnership, the assets of the Partnership, or proceeds thereof,
distributable among the holders of Class M Partnership Preferred Units shall be
insufficient to pay in full the preferential amount aforesaid and liquidating
payments on any Parity Partnership Units, then such assets, or the proceeds
thereof, shall be distributed among the holders of Class M Partnership Preferred
Units and any such Parity Partnership Units ratably in the same proportion as
the respective amounts that would be payable on such Class M Partnership
Preferred Units and any such other Parity Partnership Units if all amounts
payable thereon were paid in full. For the purposes of this Section 4, (i) a
consolidation or merger of the Partnership with one or more partnerships, or
(ii) a sale or transfer of all or substantially all of the Partnership's assets
shall not be deemed to be a liquidation, dissolution or winding up, voluntary or
involuntary, of the Partnership.

                  (b) Upon any liquidation, dissolution or winding up of the
Partnership, after payment shall have been made in full to the holders of Class
M Partnership Preferred Units and any Parity Partnership Units, as provided in
this Section 4, any other series or class or classes of Junior Partnership Units
shall, subject to the respective terms thereof, be entitled to receive any and
all assets remaining to be paid or distributed, and the holders of the Class M
Partnership Preferred Units and any Parity Partnership Units shall not be
entitled to share therein.

         5.       REDEMPTION.

         Class M Partnership Preferred Units shall be redeemable by the
Partnership as follows:

                  (a) At any time that the Previous General Partner exercises
its right to redeem all or any of the shares of Class M Preferred Stock, the
General Partner shall cause the Partnership to redeem an equal number of Class M
Partnership Preferred Units, at a redemption price per Class M Partnership
Preferred Unit equal to the same price paid by the Previous General Partner to
redeem the Class M Preferred Stock and such price shall be paid in the same
manner (including but not limited to, by means of issuance of long-term
indebtedness for purpose of such redemption) as paid by the Previous General
Partner for the Class M Preferred Stock redeemed (the "Call Date"), in the
manner set forth herein; provided, however, that in the event of a redemption of
Class M Partnership Preferred Units, if the Call Date occurs after a dividend
record date for the Class M Preferred Stock and on or prior to the related
Distribution Payment Date, the distribution payable on such Distribution Payment
Date in respect of such Class M Partnership Preferred Units called for
redemption shall be payable on such Distribution Payment Date to the holders of
record of such Class M Partnership Preferred Units on the applicable dividend
record date, and shall not be payable as part of the redemption price for such
Class M Partnership Preferred Units.

                  (b) If the Partnership shall redeem Class M Partnership
Preferred Units pursuant to paragraph (a) of this Section 5, from and after the
Call Date (unless the Partnership shall fail to make available the amount of
cash or other forms of consideration necessary to effect such redemption), (i)
except for payment of the redemption price, the Partnership shall not make any
further distributions on the Class M Partnership Preferred Units so called for
redemption, (ii) said


                                       W-3

<PAGE>   6



units shall no longer be deemed to be outstanding, and (iii) all rights of the
holders thereof as holders of Class M Partnership Preferred Units of the
Partnership shall cease except the rights to receive the cash payable upon such
redemption, without interest thereon; provided, however, that if a Call Date
occurs after a dividend record date for the Class M Preferred Stock and on or
prior to the related Distribution Payment Date, the full distribution payable on
such Distribution Payment Date in respect of such Class M Partnership Preferred
Units called for redemption shall be payable on such Distribution Payment Date
to the holders of record of such Class M Partnership Preferred Units on the
applicable dividend record date notwithstanding the prior redemption of such
Class M Partnership Preferred Units. No interest shall accrue for the benefit of
the holders of Class M Partnership Preferred Units to be redeemed on any cash
set aside by the Partnership.

         6.       STATUS OF REACQUIRED UNITS.

         All Class M Partnership Preferred Units which shall have been issued
and reacquired in any manner by the Partnership shall be deemed cancelled.

         7.       CONVERSION.

         Class M Partnership Preferred Units shall be convertible as follows:

                  (a) Upon any conversion of shares of Class M Preferred Stock
into shares of Common Stock, the General Partner shall cause a number of Class M
Partnership Preferred Units equal to the number of such converted shares of
Class M Preferred Stock to be converted by the holders thereof into Partnership
Common Units. The conversion ratio in effect from time to time for the
conversion of Class M Partnership Preferred Units into Partnership Common Units
pursuant to this Section 7 shall at all times be equal to, and shall be
automatically adjusted as necessary to reflect, the conversion ratio in effect
from time to time for the conversion of Class M Preferred Stock into Common
Stock.

                  (b) In the event of a conversion of any Class M Partnership
Preferred Units, the Partnership shall make a cash payment to the holder thereof
equal to the cash payment required to be made by the Previous General Partner to
the holder of the shares of Class M Preferred Stock the conversion of which
required the conversion of such Class M Partnership Preferred Units. Holders of
Class M Partnership Preferred Units at the close of business on a distribution
payment record date shall be entitled to receive the distribution payable on
such units on the corresponding Distribution Payment Date notwithstanding the
conversion thereof following such distribution payment record date and prior to
such Distribution Payment Date. Except as provided above, the Partnership shall
make no payment or allowance for unpaid distributions on converted units or for
distributions on the Partnership Common Units issued upon such conversion. Each
conversion of Class M Partnership Preferred Units into Partnership Common Units
shall be deemed to have been effected at the same time and date that the
corresponding conversion of Class M Preferred Stock into Common Stock is deemed
to have been effected.



                                       W-4

<PAGE>   7



                  (c) No fractional Partnership Common Units shall be issued
upon conversion of Class M Partnership Preferred Units. Instead of any
fractional Partnership Common Units that would otherwise be deliverable upon the
conversion of Class M Partnership Preferred Units, the Partnership shall pay to
the holder of such converted units an amount in cash equal to the cash payable
to a holder of an equivalent number of converted shares of Class M Preferred
Stock in lieu of fractional shares of Common Stock.

                  (d) The Partnership will pay any and all documentary stamp or
similar issue or transfer taxes payable in respect of (i) the issue or delivery
of Partnership Common Units or other securities or property on conversion or
redemption of Class M Partnership Preferred Units pursuant hereto, and (ii) the
issue or delivery of Common Stock or other securities or property on conversion
or redemption of Class M Preferred Stock pursuant to the terms hereof.

         8.       RANKING.

         Any class or series of Partnership Units of the Partnership shall be
deemed to rank:

                  (a) prior or senior to the Class M Partnership Preferred
Units, as to the payment of distributions and as to distributions of assets upon
liquidation, dissolution or winding up, if the holders of such class or series
shall be entitled to the receipt of distributions and of amounts distributable
upon liquidation, dissolution or winding up, as the case may be, in preference
or priority to the holders of Class M Partnership Preferred Units ("Senior
Partnership Units");

                  (b) on a parity with the Class M Partnership Preferred Units,
as to the payment of distributions and as to distribution of assets upon
liquidation, dissolution or winding up, whether or not the distribution rates,
distribution payment dates or redemption or liquidation prices per unit or other
denomination thereof be different from those of the Class M Partnership
Preferred Units if (i) such class or series of Partnership Units shall be Class
B Partnership Preferred Units, Class C Partnership Preferred Units, Class D
Partnership Preferred Units, Class G Partnership Preferred Units, Class H
Partnership Preferred Units, Class I Partnership Preferred Units, Class J
Partnership Preferred Units, Class K Partnership Preferred Units, Class L
Partnership Preferred Units, Class One Partnership Preferred Units, or Class Two
Partnership Preferred Units or (ii) the holders of such class or series of
Partnership Units and the Class M Partnership Preferred Units shall be entitled
to the receipt of distributions and of amounts distributable upon liquidation,
dissolution or winding up in proportion to their respective amounts of accrued
and unpaid distributions per unit or other denomination or liquidation
preferences, without preference or priority one over the other (the Partnership
Units referred to in clauses (i) and (ii) of this paragraph being hereinafter
referred to, collectively, as "Parity Partnership Units"); and

                  (c) junior to the Class M Partnership Preferred Units, as to
the payment of distributions and as to the distribution of assets upon
liquidation, dissolution or winding up, if (i) such class or series of
Partnership Units shall be Partnership Common Units or Class I High Performance
Partnership Units or (ii) the holders of Class M Partnership Preferred Units
shall be

                                       W-5

<PAGE>   8



entitled to receipt of distributions or of amounts distributable upon
liquidation, dissolution or winding up, as the case may be, in preference or
priority to the holders of such class or series of Partnership Units (the
Partnership Units referred to in clauses (i) and (ii) of this paragraph being
hereinafter referred to, collectively, as "Junior Partnership Units").

         9.       SPECIAL ALLOCATIONS.

                  (a) Gross income and, if necessary, gain shall be allocated to
the holders of Class M Partnership Preferred Units for any Fiscal Year (and, if
necessary, subsequent Fiscal Years) to the extent that the holders of Class M
Partnership Preferred Units receive a distribution on any Class M Partnership
Preferred Units (other than an amount included in any redemption pursuant to
Section 5 hereof) with respect to such Fiscal Year.

                  (b) If any Class M Partnership Preferred Units are redeemed
pursuant to Section 5 hereof, for the Fiscal Year that includes such redemption
(and, if necessary, for subsequent Fiscal Years) (a) gross income and gain (in
such relative proportions as the General Partner in its discretion shall
determine) shall be allocated to the holders of Class M Partnership Preferred
Units to the extent that the redemption amounts paid or payable with respect to
the Class M Partnership Preferred Units so redeemed exceeds the aggregate
Capital Contributions (net of liabilities assumed or taken subject to by the
Partnership) per Class M Partnership Preferred Unit allocable to the Class M
Partnership Preferred Units so redeemed and (b) deductions and losses (in such
relative proportions as the General Partner in its discretion shall determine)
shall be allocated to the holders of Class M Partnership Preferred Units to the
extent that the aggregate Capital Contributions (net of liabilities assumed or
taken subject to by the Partnership) per Class M Partnership Preferred Unit
allocable to the Class M Partnership Preferred Units so redeemed exceeds the
redemption amount paid or payable with respect to the Class M Partnership
Preferred Units so redeemed.

         10.      RESTRICTIONS ON OWNERSHIP.

         The Class M Partnership Preferred Units shall be owned and held solely
by the General Partner or the Special Limited Partner.

         11.      GENERAL.

                  (a) The ownership of Class M Partnership Preferred Units may
(but need not, in the sole and absolute discretion of the General Partner) be
evidenced by one or more certificates. The General Partner shall amend Exhibit A
to the Agreement from time to time to the extent necessary to reflect accurately
the issuance of, and subsequent conversion, redemption, or any other event
having an effect on the ownership of, Class M Partnership Preferred Units.

                  (b) The rights of the General Partner and the Special Limited
Partner, in their capacity as holders of the Class M Partnership Preferred
Units, are in addition to and not in limitation of any other rights or authority
of the General Partner or the Special Limited Partner,


                                       W-6

<PAGE>   9


respectively, in any other capacity under the Agreement or applicable law. In
addition, nothing contained herein shall be deemed to limit or otherwise
restrict the authority of the General Partner or the Special Limited Partner
under the Agreement, other than in their capacity as holders of the Class M
Partnership Preferred Units.


                                       W-7