  In this paper, we study a double scaling limit of two multi-matrix models:
the $U(N)^2 \times O(D)$-invariant model with all quartic interactions and the
bipartite $U(N) \times O(D)$-invariant model with tetrahedral interaction ($D$
being here the number of matrices and $N$ being the size of each matrix). Those
models admit a double, large $N$ and large $D$ expansion. While $N$ tracks the
genus of the Feynman graphs, $D$ tracks another quantity called the grade. In
both models, we rewrite the sum over Feynman graphs at fixed genus and grade as
a finite sum over combinatorial objects called schemes. This is a result of
combinatorial nature which remains true in the quantum mechanical setting and
in quantum field theory. Then we proceed to the double scaling limit at large
$D$, i.e. for vanishing grade. In particular, we find that the most singular
schemes, in both models, are the same as those found in Benedetti et al. for
the $U(N)^2 \times O(D)$-invariant model restricted to its tetrahedral
interaction. This is a different universality class than in the 1-matrix model
whose double scaling is not summable.
