  We expand the two-photon Hong-Ou-Mandel (HOM) effect onto a
higher-dimensional set of spatial modes and introduce an effect that allows
controllable redistribution of quantum states over these modes using
directionally unbiased linear-optical four-ports without post-selection. The
original HOM effect only allows photon pairs to exit in two directions in
space. But when accompanied by beam splitters and phase shifters, the result is
a directionally controllable two-photon HOM effect in four spatial modes, with
direction controlled by changing the phases in the system. This controllable
quantum amplitude manipulation also allows demonstration of a "delayed" HOM
effect by exploiting phase shifters in a system of two connected multiport
devices. By this means, both spatial and temporal control of the propagation of
the two-photon superposition state through a network can be achieved.
