User blog comment:Billicusp/Extending ExE to absurd heights/@comment-27513631-20160217224635

This, if properly defined, looks limited at $$\varphi(\omega^2,0,0,0)$$ to me. Maybe higher, probably lower; I can't really tell what you're doing here. Definitely less than $$\varphi(\omega^{\omega^\omega},0,0,0)$$.