Dic: be that as it may

• ‘Is he still just as fat?’--‘I wouldn't know,’ continued her mother, ignoring the interruption,  ‘and be that as it may, he has made a fortune.’ 
• Be that as it may, I still think he should come. 
• Building a new children's home will cost a lot of money but, be that as it may, there is an urgent need for the facility.
• ‘He was only joking.’ ‘Be that as it may, silly remarks like that can do a lot of harm.’
• I know that he tries hard; be that as it may, his work just isn't good enough.

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How can its usage de defined:

COBUILD▶ You say `Be that as it may' when you want to move onto another subject or go further with the discussion, without deciding whether what has just been said is right or wrong.

COLLINS▶ in spite of that: a sentence connector conceding the possible truth of a previous statement and introducing an adversative clause

CALD▶ (SLIGHTLY FORMAL) used to mean that you accept that a piece of information is true but it does not change your opinion of the subject you are discussing.

LDOCE▶ formal. used to say that even though you accept that something is true, it does not change a situation

OALD▶ despite that (synonym nevertheless)


CF. conceding a point and making a counterargument (OALD)