User blog comment:PsiCubed2/Does anybody here know the expansion rules for BM2?/@comment-35470197-20180709144339

Koteitan made a list classifying seven variants of BM's and containing (guess of) expansion rules of them. For example, it deals with BM2.

http://ja.googology.wikia.com/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:Koteitan/%E3%83%90%E3%82%B7%E3%82%AF%E8%A1%8C%E5%88%97%E3%81%AE%E4%BA%9C%E7%A8%AE%E3%83%AB%E3%83%BC%E3%83%AB%E3%81%AE%E5%88%86%E9%A1%9E

But written in Japanese.