In On the Axiom of Extensionality, Part II, JSL, Vol. 24, No. 4, 287-300, R. O. Gandy shows that NBG set theory minus extensionality interprets NBG set theory. His systems make use of set abstracts, unlike the related result of Dana Scott, that ZFC minus extensionality interpret ZFC, in More on the Axiom of Extensionality, Essays on the Foundations of Mathematics, dedicated to A. A. Fraenkel, 1962, 115-131.

May Gandy's argument be extended to NBG minus the power set axiom?