I would like to ask if I have got the meaning of the expression "for that matter" (as far as is concerned)
I am eating sushi now, raw fish, for that matter.
She has been studying hard. Ten hours a day for that matter.
He was not an English native speaker; for that matter, he was from France. He might have made several mistakes.
For that matter, I am not a native speaker either.
Is there another expression or synonim that means the same?
Thanks in advance