Canine, say, barking regardless (2,3,4)
I believe the answer is:
in any case
'regardless' is the definition.
(thesaurus)
'canine say barking' is the wordplay.
'barking' indicates an anagram (UK slang for mad).
'canine'+'say'='caninesay'
'caninesay' is an anagram of 'IN ANY CASE'.
(Other definitions for in any case that I've seen before include "Where customs officers may search" , "No matter what" , "Where a customs officer may search" , "Lawyers may be so employed" , "At all events" .)