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fit on (something)
To attach or place something onto something else. A noun or pronoun can be used between "fit" and "on." I can't fit on these gloves—are you sure they're mine? You know, you can adjust that wrench if you can't fit it on the nut.
fit something on(to) somethingand fit something on
to manage to place something onto something. See if you can fit this lid onto that jar over there. Sorry, I can't fit on this lid, because it's too big.