grow together vs mix

grow together is not a noun while mix is a noun.

Word	Noun	Adjective	Verb	Adverb
grow together	No	No	Yes	No
mix	Yes	No	Yes	No

As verbs, mix is a hypernym of grow together; that is, mix is a word with a broader meaning than grow together:

Other hypernyms of grow together include blend, coalesce, combine, commingle, conflate, flux, fuse, immix, meld, merge.

grow together (noun)	mix (noun)
	the act of mixing together
	an event that combines things in a mixture
	a commercially prepared mixture of dry ingredients

grow together (verb)	mix (verb)
grow together (of plants and organs)	mix together different elements
	add as an additional element or part
	combine (electronic signals)
	to bring or combine together or with something else
	mix so as to make a random order or arrangement
	open (a place) to members of all races and ethnic groups