Oh that's a difficult one for so long, but I am pretty sure most garages outside of the center would be more than glad to offer the service.
Off the top of my head, I'd recommend contacting these two:
Scegli il parcheggio in centro a Firenze più comodo e prenota la tua sosta sicura comodamente online, a prezzi bassi. Affidati a Central Parking!
They are companies that own several garages each, some in the center and others just outside. Between either, they have the space for 3 cars so they might have each at a separate location. In any case, they all are COVERED and always have personnel so they'd also be secure.
Let us know whether they offer a good price for those 3 months, I'd be interested in knowing how well they are in offering customized services and how they respond to queries such as yours. Hope you find the right place for you!