Context
In the work of Baker, Gill, Solovay, we know that there exists some oracle A s.t.
$$P^A = NP^A$$.
Now, in CCAMA, this oracle $A$ is given as an EXP complete language.
Question:
Can we do this with something weaker? Say a PSPACE-complete language, like quantified boolean formulas? Intuitively, it seems that if we have the power of the polynomial hierarchy, all what $NP^{PSPACE}$ really does is add an extra layer of quantifiers, which thus is contained in $PSPACE$, and contained in $P^{PSPACE}$.
Thanks!