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 $$\operatorname {MG}(X)= E \cap (\operatorname {trs}(X) \times \operatorname {trs}(X))$$; Where $E = \{(x,y)\mid x \in y\}$

Now what I want to do is to instead of just stipulating Extensionality over $\sf SF$, 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 $\sf Strong \ NF$?