  We consider a new large-N limit, in which the 't Hooft coupling grows with N.
We argue that a class of large-N equivalences, which is known to hold in the 't
Hooft limit, can be extended to this very strongly coupled limit. Hence this
limit may lead to a new way of studying corrections to the 't Hooft limit,
while keeping nice properties of the latter. As a concrete example, we describe
large-N equivalences between the ABJM theory and its orientifold projection.
The equivalence implies that operators neutral under the projection symmetry
have the same correlation functions in two theories at large-N. Usual field
theory arguments are valid when 't Hooft coupling $\lambda\sim N/k$ is fixed
and observables can be computed by using a planar diagrammatic expansion. With
the help of the AdS/CFT correspondence, we argue that the equivalence extends
to stronger coupling regions, $N\gg k$, including the M-theory region $N\gg
k^5$. We further argue that the orbifold/orientifold equivalences between
certain Yang-Mills theories can also be generalized. Such equivalences can be
tested both analytically and numerically. Based on calculations of the free
energy, we conjecture that the equivalences hold because planar dominance
persists beyond the 't Hooft limit.
