For that matter
Definition 1 of 1
Pro Tip 1/3Emphasize Similarity
Use it to stress that two or more situations are similarly true or applicable. 
He's never visited France, or Spain for that matter.
Pro Tip 2/3Broaden Scope
It can expand the discussion to include related subjects or areas. 
Their team doesn't play well at home, or away for that matter.
Pro Tip 3/3Clarify Limits
It’s often used to clarify the extent or limit of a statement. 
She doesn't eat meat, or any animal products for that matter.