User blog comment:PsiCubed2/For Newbies (and Veterans too): The Great Scale of Googology/@comment-32783837-20180226034300/@comment-30754445-20180226061216

Even if Taranovsky goes beyond ZFC (which is quite unlikely), we know for certain that it has an upper bound of ZFC+"there is a measurable ordinal".

I highly doubt that such variations of ZFC should be placed much higher than 400.