overflow vs brim over

overflow is a noun but brim over is not a noun.

Word	Noun	Adjective	Verb	Adverb
overflow	Yes	No	Yes	No
brim over	No	No	Yes	No

As verbs, overflow and brim over are synonyms defined as:

Other synonyms of overflow include overrun, run over, well over.

overflow (noun)	brim over (noun)
a large flow
the occurrence of surplus liquid (as water) exceeding the limit or capacity

overflow (verb)	brim over (verb)
overflow with a certain feeling	flow or run over (a limit or brim)
flow or run over (a limit or brim)