Let's work in Quine's $\sf ML$, we can define classes after nonstratified formulas. Now for every set $X$ we can define the membership graph $\operatorname {MG}(X)$ on its transitive closure, that is the restriction of the graph of membership relation (which is a class) to the transitive closure class of $X$, so $$\operatorname {MG}(X)= E \cap (\operatorname {trscl}(X) \times \operatorname {trscl}(X))$$; Where $E = \{(x,y) \mid x \in y, x \in V, y \in V\}$

Now what I want to do is to instead of just stipulating Extensionality over $\sf SF$ (i.e.; $\sf NF-Extensionality$), we stipulate:

$$ \operatorname {MG}(X) \approx \operatorname {MG}(Y) \to X=Y.$$

where $(,)$ is defined after Wiener pairs; and $\approx$ stand for graph ismorphism.

I'd label this axiom as Strong Extensionality, and "Strong Extensionality + Stratified Comprehension" as $\sf Strong \ NF$.

Clearly Strong Extensionality proves Extensionality. But if we assume that $\sf NF$ is consistent, then would this be enough to prove the consistency of $\sf Strong \ NF$?