Rifarne is a compound verb formed from rifare (to remake, to do again) and the pronoun ne (of it/them). It means "to remake it" or "to make it again from something."
In the song, the lyrics say "Prendine abbastanza per rifarne uno per te" (Take enough of them to remake one for you). The singer is metaphorically broken into a thousand pieces and asks the loved one to gather enough of these pieces to remake a new version of him, without his flaws. It's a poignant and unique way to express transformation and self-sacrifice for love.
"Amore Che Torni" ("Love, You Who Return") is about welcoming someone back without pretending nothing happened. The singer isn't asking for the old version of themselves back, flaws and habits included. Instead they tell this returning love to look for what's left of them scattered elsewhere: in other people's eyes, in torn-up verses, in a room filled with fragments.
There's a quiet condition running through the whole song. Come back if you really mean it, but don't expect to find what you don't remember. Choose a new way to think of the singer rather than trying to change them into who they used to be.
By the end, the singer offers everything they have left to give, plainly and without excuses. It isn't much anymore, but it's honest, and it's all they've got.