Realistic? Sure, but not without risk. Obviously the best option is to book all on one ticket, utilizing an airlines partners to get there, but maybe too late for that (If your airline and ticket class allows changes, I would at least check with them first).
Otherwise the calculation is how much time to allow between landing and your next flight. Will your flight be on time, how much time to get through immigration, will you have checked bags (requires exiting, getting bags, re-checking bags, back through security), how far is the next terminal?
Most of the time, doing this means leaving a healthy buffer (3, 4, 5 hours?), likely sitting in an airport after a long flight for most of those hours, and of course the risk that things do not go right, meaning your ticket is mostly useless and stuck coming up with plan B.
If you decide it is worth the risk, know what your options are, maybe spring for a more expensive ticket class from Rome to Palermo, one that might allow a change or later flight, or at least a refund.