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Rome visa-free transit area: Can I move between Terminals 1-3 freely?
Most likely no. This is a self transfer and you are responsible for having the required documentation which in this case will most likely means "you need to be able to legally enter Italy" It's highly unlikely that Latam will let you board otherwise. Whether you have a second ticket is immaterial to them.
Kiwi is clear about this: https://www.kiwi.com/en/help/kiwi-com-travel-hacks-258/article/self-transfer-travel-hack-131/
You might need to leave the visa-free zone (the area behind security control, where the gates are) during layover to recheck your baggage, check in for your next flight, change terminals, or simply because of the airportβs design.