  Perfect ideals of grade 3 can be classified based on algebra structures on
their minimal free resolutions. The classification is incomplete in the sense
that it remains open which of the possible algebra structures actually occur;
this realizability question was formally posed by Avramov in 2012. Of five
classes of algebra structures, the realizability question has been answered for
one class. In this work, we answer the realizability question for two classes
and contribute towards an answer for a third.
