  In the past two decades, extensive research has been conducted on the
(co)homology of various models of random simplicial complexes. So far, it has
always been examined merely as a list of groups. This paper expands upon this
by describing both the ring structure and the Steenrod-algebra structure of the
cohomology of the multiparametric models. For the lower model, we prove that
the ring structure is always a.a.s trivial, while, for certain parameters, the
Steenrod-algebra a.a.s acts non-trivially. This reveals that complex
multi-dimensional topological structures appear as subcomplexes of this model.
In contrast, we improve upon a result of Farber and Nowik, and assert that the
cohomology of the upper multiparametric model is a.a.s concentrated in a single
dimension.
