[Idiom] For that matter

[LeighS]

Hello fellow teachers!
I'm a bit stuck and hope to find a bit more clarification on 'for that matter'. I seem to going round in circles and not getting anywhere with the reference material I have. I need to analyse 'for that matter' in terms of;
synonyms, context, register, connotation, style, syntax, reference, collocation, phonology etc.....

Any help would be greatly appreciated!

[abdmlkbd]

give a search [writing: "For that matter"] in this link:
Idioms and phrases
and you'll (i hope, because i already checked and found!) find some useful stuff.

[LeighS]

Thanks, I've already done a search on the site, but didn't find what I was looking for.