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Given $ZFC^{-}$, that is, ZFC-Powerset+Collection+Separation, are there a set of alternative axioms $X$ (other than the trivial one, namely, Powerset) that, when added to $ZFC^{-}$, allow one to derive Powerset as a theorem of $ZFC^{-}$+$X$ and recover full $ZFC$? (Thanks to Prof. Hamkins for setting me straight on the correct formulation of $ZFC^{-}$.)

Given $ZFC^{-}$, that is, ZFC-Powerset+Collection+Separation, is there a set of alternative axioms $X$ (other than the trivial one, namely, {Powerset}) that, when added to $ZFC^{-}$, allow one to derive Powerset as a theorem of $ZFC^{-}$+$X$ and recover full $ZFC$? (Thanks to Prof. Hamkins for setting me straight on the correct formulation of $ZFC^{-}$.)

Given $ZFC^{-}$, that is, ZFC-Powerset+Collection+Separation, are there a set of alternative axioms $X$ (other than the trivial one, namely, Powerset) that, when added to $ZFC^{-}$, allow one to derive Powerset as a theorem of $ZFC^{-}$+$X$ and recover full $ZFC$? (Thanks to Prof. Hamkins for setting me straight on the correct formulation of $ZFC^{-}$).

Given $ZFC^{-}$, that is, ZFC-Powerset+Collection+Separation, are there a set of alternative axioms $X$ (other than the trivial one, namely, Powerset) that, when added to $ZFC^{-}$, allow one to derive Powerset as a theorem of $ZFC^{-}$+$X$ and recover full $ZFC$? (Thanks to Prof. Hamkins for setting me straight on the correct formulation of $ZFC^{-}$.)

Given $ZFC^{-}$, that is, ZFC-Powerset-Replacement+Collection, are there a set of alternative axioms $X$ (other than the trivial ones, namely, Powerset and Replacement) that, when added to $ZFC^{-}$, allow one to derive Powerset and Replacement as theorems of $ZFC^{-}$+$X$ and recover full $ZFC$?

Given $ZFC^{-}$, that is, ZFC-Powerset+Collection+Separation, are there a set of alternative axioms $X$ (other than the trivial one, namely, Powerset) that, when added to $ZFC^{-}$, allow one to derive Powerset as a theorem of $ZFC^{-}$+$X$ and recover full $ZFC$? (Thanks to Prof. Hamkins for setting me straight on the correct formulation of $ZFC^{-}$).