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This paper is the result of a research project completed in the context ofthe first author's Undergraduate Student Research Award from the NaturalSciences and Engineering Research Council of Canada (NSERC).  We prove a nesting phenomenon for twisted Frobenius extensions. Namely,suppose $R \subseteq B \subseteq A$ are graded superrings such that $A$ and $B$are both twisted Frobenius extensions of $R$, $R$ is contained in the center of$A$, and $A$ is projective over $B$. Our main result is that, under theseassumptions, $A$ is a twisted Frobenius extension of $B$. This generalizes aresult of Pike and the second author, which considered the case where $R$ is afield.

Nested Frobenius extensions of graded superrings