Hi Michael The first option is not possible We can never say be being doing. I can say "I have BEEN doing" but not be being.. Please give me the full sentence or context for a better explanation.

Generally we say "being done,to be done,to be doing “ etc. I'm not sure "to be being doing" has some problems but i just feel it's a little weird.

Thank you very much, Peachey!

Michael, I've found the original sentence you mentioned, and there are a couple of other awkward phrases by the same commenter. I really doubt that person is native (ie. grew up and was educated in the UK, as the original blog is UK-based), although half of his comment was reasonably OK. It's better to look for other examples before assuming a phrase is correct English.