  We explore whether the phase diagram of tensor models could feature a
pregeometric, discrete and a geometric, continuum phase for the building blocks
of space. The latter are associated to rank $d$ tensors of size $N$. We search
for a universal large $N$ scaling limit in a rank-3 model with real tensors
that could be linked to a transition between the two phases. We extend the
conceptual development and practical implementation of the flow equation for
the pregeometric setting. This provides a pregeometric "coarse-graining" by
going from many microscopic to few effective degrees of freedom by lowering
$N$. We discover several candidates for fixed points of this coarse graining
procedure, and specifically explore the impact of a novel class of interactions
allowed in the real rank-3 model. In particular, we explain how most
universality classes feature dimensional reduction, while one candidate,
involving a tetrahedral interaction, might potentially be of relevance for
three-dimensional quantum gravity.
