Tunneling EAP-TTLS over EAP-TTLS?

This question may come across as slightly (completely) absurd, but please entertain me as I believe it may have some pedagogical value, or if not at least some mild distraction on what is normally quite a serious site.

EAP-TTLS lists among its phase 2 authentication protocols a further layer of EAP.

This seems nicely recursive, and I wonder if it could lead to frustrating inception-like possibilities whereby one ends up tunneling EAP-TTLS over EAP-TTLS over EAP-TTLS over EAP-TTLS over ...

Obviously this would have limits, similar to classical recursion whereby the number of recursed states exceed the capability to contain them, generally a stack overflow. Specifically in this case I think the overhead of the headers at the asymptotic layer would exceed the capability of the fragmentation algorithm to carry them (I guess the precise number at which this occurs would be an interesting question for a masters student).

But is there anything more immediate than this that could limit this recursion? I suspect there are factors that would prevent even a single layer of recursion occuring.