toy vs toy with

toy is a noun but toy with is not a noun.

Word	Noun	Adjective	Verb	Adverb
toy	Yes	No	Yes	No
toy with	No	No	Yes	No

toy (noun)	toy with (noun)
any of several breeds of very small dogs kept purely as pets
an artifact designed to be played with
a copy that reproduces a person or thing in greatly reduced size
a nonfunctional replica of something else (frequently used as a modifier)
a device regarded as providing amusement

toy (verb)	toy with (verb)
engage in an activity as if it were a game rather than take it seriously	take into consideration, have in view
manipulate manually or in one's mind or imagination
behave carelessly or indifferently