The small numbers of z > 1 galaxies in new faint galaxy samples challenges the assumption that their mass function does not evolve significantly up to z = 1. A " maximal " evolutionary model for the faint galaxy population is proposed, wherein galaxies form in preexisting halos, and merger dynamics is used to allow for interaction induced star formation and the change in M*. Interactions at z less than or similar 0.5 mainly brighten and blue galaxies, with little change in numbers. Beyond z greater than or similar to 0.5, merging begins to reduce the characteristic mass and increase the numbers of galaxies. As observational predictions the model requires that (1) the current mass doubling time scale of M* galaxies is congruent 1.5t0, which is uncomfortably short; (2) the merger rate, at low redshift, increases approximately as (1 + z)4 (for OMEGA = 1); and (3) at z = 1, the characteristic galaxy mass is about 25% of the z = 0 value; hence, galaxies having circular velocities of greater than or similar to 200 km s-1 are relatively rare beyond z > 1, although such halos likely exist in abundance. The spirit of the calculation is to provide a testable, but perhaps somewhat extreme, hypothesis in which gravitational interactions limit the rate of formation activity.