See: https://softwarefreedom.org/resources/2007/gpl-non-gpl-colla...
The MIT license gives you a right to sublicense to your heart's content.
"A more complicated case occurs when a developer makes copyrightable changes to a permissive-licensed file that the developer is incorporating into a GPL’d program"
"Note, however, that in a single source file it is typically very difficult, and often completely infeasible, to determine which parts of such a file are covered by permissive terms."
The point being that perhaps you can relicense it, but does that accomplish what you want...making some particular part of it fully bound by the GPL? That's the complicated part.
This is just taking the full project wholesale and relicensing the whole thing under GPL.
Licenses are granted based upon You meeting the qualified criteria as stated.