Be that as it may, everybody is in good health (3,4,4)
I believe the answer is:
all very well
'be that as it' is the definition.
I know nothing about this answer so I can't tell whether it can be defined by this definition.
'everybody is in good health' is the wordplay.
'everybody' becomes 'all' (all people).
'is in good health' becomes 'verywell' (I can't explain this - if you can you should give a lot more credence to this answer).
'all'+'verywell'='ALL VERY WELL'
'may' is the link.
Can you help me to learn more?
(Other definitions for all very well that I've seen before include "Phrase often introducing an objection" , "that's fine as far as it goes" , "Ironic expression of discontent" , "make an ironic objection" , "utterly brilliantly delivered" .)