We know that if you have a PSPACE machine, it's powerful enough to give an interactive proof of any level the polynomial hierarchy. (And if I remember right, all you need is #P.) But suppose you want to give an interactive proof of membership in a $\Sigma_2$ language. Is it enough to be able to solve problems in $\Sigma_2$? Is solving problems in $\Sigma_5$ adequate? More generally, if you can solve $\Sigma_k$ or $\Pi_k$ problems, for what $\Sigma_\ell$ is this sufficient to generate interactive proofs of all languates in $\Sigma_\ell$?
This question was inspired by this cstheory stackexchange question.