  In this paper, we consider the iterated trimming complex associated to data
yielding a complex of length $3$. We compute an explicit algebra structure in
this complex in terms of the algebra structures of the associated input data.
Moreover, it is shown that many of these products become trivial after
descending to homology. We apply these results to the problem of realizability
for Tor-algebras of grade $3$ perfect ideals, and show that under mild
hypotheses, the process of "trimming" an ideal preserves Tor-algebra class. In
particular, we construct new classes of ideals in arbitrary regular local rings
defining rings realizing Tor-algebra classes $G(r)$ and $H(p,q)$ for a
prescribed set of homological data.
