<PAGE>   1
                                                                  EXHIBIT 10(m)




                               SECOND AMENDMENT TO
                    FIRST AMENDED AND RESTATED LOAN AGREEMENT

          This Second Amendment to First Amended and Restated Loan Agreement
("Amendment") is entered into as of the 31st day of March, 1999, by Response
Oncology, Inc. ("Borrower"), a Tennessee corporation; Union Planters Bank, N.A.
("Union Planters"), a national banking association formerly known as Union
Planters National Bank; AmSouth Bank ("AmSouth"), a Tennessee banking
corporation formerly known as AmSouth Bank of Tennessee; and NationsBank, N.A.
("NationsBank"), a national banking association formerly known as NationsBank of
Tennessee, N.A., in its individual capacity and as Agent for itself, Union
Planters and AmSouth; and Response Oncology of West Ft. Lauderdale, Inc.,
Response Oncology of Treasure Coast, Inc., Response Oncology of Miami Beach,
Inc., Response Oncology of Tamarac, Inc., Response Oncology of St. Petersburg,
Inc. and Response Oncology of Fort Lauderdale, Inc., each being Florida
corporations (collectively the "Guarantors")

                                R E C I T A L S:

          WHEREAS, NationsBank, Union Planters, AmSouth and Borrower have 
previously executed that First Amended and Restated Loan Agreement dated as of
April 21, 1997, as amended by that First Amendment to First Amended and Restated
Loan Agreement dated as of March 31, 1998, and as further amended by that
certain letter from Agent to Borrower dated June 25, 1998 (as amended, the "Loan
Agreement"); and

          WHEREAS, the Guarantors have guaranteed the indebtedness and other
obligations of Borrower under the Loan Agreement; and

          WHEREAS, certain Events of Default have occurred under the Loan
Agreement; and

          WHEREAS, the parties wish to make certain agreements regarding the
outstanding Events of Default and to extend the maturity of the credit provided
for under the Loan Agreement;

          NOW, THEREFORE, for valuable consideration, the receipt and 
sufficiency of which are acknowledged, the parties agree as follows:

          1. Loan Agreement References. Capitalized terms not defined herein 
have the meanings set forth in the Loan Agreement. The provisions of this
Amendment shall control over provisions of the Loan Agreement to the extent
inconsistent therewith.

          2. Extension of Maturity. The Loan Agreement is hereby amended by 
deleting the current definition of "Maturity Date" and in its place inserting
the following language:

             "Maturity Date" means June 30, 1999.



<PAGE>   2



          3. Freeze of Loan Balance. Borrower agrees not to request, and the
Lenders shall not be obligated to extend, any additional Loans under any
circumstances. All Loans presently outstanding shall be regarded as Prime Rate
Loans. LIBOR Loans shall not be permitted.

          4. Resumption of Monthly Financial Reports. The Loan Agreement is 
hereby amended by deleting the final sentence of Section 5.3.1 thereof, thus
reinstating the requirement that Borrower deliver monthly financial reports
beginning with the reports for the month of March, 1999.

          5. Waiver of Certain Events of Default. Lenders hereby waive the
Events of Default that would otherwise presently exist under Sections 7.1
(Current Ratio), 7.3 (Total Funded Debt to Consolidated EBITDA) and 7.4 (Fixed
Charge Coverage) of the Loan Agreement due to the financial condition of
Borrower as of December 31, 1998 and March 31, 1999.

          6. EBITDA Requirement. The Loan Agreement is hereby amended by adding 
the following provision as a new Section 7.7 thereof:

             Borrower shall maintain Consolidated EBITDA of at least $1,100,000
             for March of 1999 and each subsequent month.

          7. Extension Fees. Borrower shall pay to Agent for the account of
Lenders extension fees of $30,000 concurrently with the execution hereof and,
unless the Loans have been previously repaid in full, an additional $45,000 on
May 1, 1999 and $60,000 on June 1, 1999.

          8. Expenses. Concurrently with the execution hereof, Borrower shall 
pay all of the fees and expenses of Agent's attorneys relating to the Loan
Agreement and this Amendment.

          9. Conditions to Closing. This Amendment shall become effective only
upon Borrower's delivery to Agent of the following fully executed documents, in
form and substance acceptable to Agent:

             (a)  This Amendment.

             (b)  First Amendments to Revolving Credit Notes for each of the
Lenders, extending the maturity thereof to June 30, 1999.

             (c)  Certified Copy of Resolutions of Borrower's and each
Guarantor's Board of Directors authorizing the execution and delivery of this
Amendment and related documents.

             (d)  Opinion letter issued by Borrower's and the Guarantors' 
outside counsel confirming the existence and corporate authority of Borrower and
the Guarantors; the due authorization, execution and delivery of this Amendment
and the related documents; the


                                      - 2 -


<PAGE>   3



enforceability hereof; the noncontravention of this Amendment with Borrower's
and Guarantors' constituent documents, laws, orders and agreements; and the
absence of any material litigation against Borrower or any Guarantor.

             (e)   Monthly financial statements (in form and substance as 
described in Section 3.5.1 of the Loan Agreement) for the months of January and
February, 1999, which must disclose that Borrower had at least $1,100,000 of
Consolidated EBITDA for each of those months.

             (f)   Closing Statement evidencing the approval and payment of all
fees and expenses due from Borrower in connection with this Amendment.

          10. Validity of Loan Documents. As modified and amended hereby, the
Loan Documents shall remain in full force and effect. Borrower and the
Guarantors warrant and represent that (a) the Loan Documents are valid, binding
and enforceable against Borrower and the Guarantors according to their terms,
subject to principles of equity and laws applicable to the rights of creditors
generally, including bankruptcy laws, (b) the security interests previously
granted in the Loan Documents are and remain perfected and continue to secure
the Obligations with the priority required by the Loan Documents, and (c) after
giving effect to this Amendment, no default or Event of Default presently exists
under the Loan Documents and no condition presently exists which, with the
giving of notice, the passing of time, or both, would cause such a default or
Event of Default. Borrower and the Guarantors further acknowledge that their
obligations evidenced by the Loan Documents are not subject to any counterclaim,
defense or right of setoff, and Borrower and the Guarantors hereby release
Lenders and Agent and their respective officers, directors, agents, attorneys
and employees from any such claim, known or unknown, that Borrower or the
Guarantors may have against any or all of them as of the execution of this
Amendment.

          11. Governing Law: Venue, Etc.. The validity, construction and
enforcement hereof shall be determined according to the substantive laws of the
State of Tennessee. Venue, procedures for dispute resolution and other such
matters with respect to this Amendment shall be governed by the provisions of
the Loan Agreement.

          12. Method of Execution. This Amendment shall be effective upon the
parties' delivery to Agent of signed originals or telecopies hereof as signed;
provided, however, each party who initially delivers by telecopy shall also
immediately forward an executed original hereof to Agent. The failure of any
party to so provide Agent with an original hereof shall not impair the validity
of this Amendment, but shall entitle Agent to obtain specific performance of the
obligation to provide an executed original of this Amendment.


                                      - 3 -


<PAGE>   4



                  Executed effective as of the date stated above.



                                              RESPONSE ONCOLOGY, INC.

                                              By:
                                                 -----------------------------
                                              Title:
                                                    --------------------------


                                              NATIONSBANK, N.A. (formerly
                                              known as NationsBank of Tennessee,
                                              N.A.), as Lender and as Agent

                                              By:
                                                 -----------------------------
                                              Title: Senior Vice President
                                                    --------------------------


                                              UNION PLANTERS BANK, N.A.

                                              By:
                                                 -----------------------------
                                              Title:
                                                    --------------------------

                                              AMSOUTH BANK

                                              By: 
                                                 -----------------------------
                                              Title:
                                                    --------------------------
                                  
                                              RESPONSE ONCOLOGY OF WEST
                                              FT. LAUDERDALE, INC.

                                              By:
                                                 -----------------------------
                                              Title:
                                                    --------------------------

                                              RESPONSE ONCOLOGY OF
                                              TREASURE COAST, INC.

                                              By:
                                                 -----------------------------
                                              Title: 
                                                    --------------------------
                                              RESPONSE ONCOLOGY OF MIAMI
                                              BEACH, INC.

                                              By:
                                                 -----------------------------
                                              Title: 
                                                    --------------------------

       [Signature page to Second Amendment to First Amended and Restated
                                 Loan Agreement]




                                      - 4 -


<PAGE>   5



                                               RESPONSE ONCOLOGY OF
                                               TAMARAC, INC.

                                               By:
                                                  -----------------------------
                                               Title: 
                                                     --------------------------

                                               RESPONSE ONCOLOGY OF ST.
                                               PETERSBURG, INC.

                                               By:
                                                  -----------------------------
                                               Title:
                                                     --------------------------


                                               RESPONSE ONCOLOGY OF FORT
                                               LAUDERDALE, INC.

                                               By:
                                                  -----------------------------
                                               Title: 
                                                     --------------------------


        [Signature page to Second Amendment to First Amended and Restated
                                Loan Agreement]




                                      - 5 -