take someone's side vs take sides with

take someone's side and take sides with both are verbs.

Word	Noun	Adjective	Verb	Adverb
take someone's side	No	No	Yes	No
take sides with	No	No	Yes	No

As verbs, take someone's side and take sides with are synonyms defined as:

take someone's side and take sides with: support someone (as in an argument)

take someone's side (verb)	take sides with (verb)
support someone (as in an argument)	support someone (as in an argument)