Totally possible to visit the same place 2, 5 or 10 times : the only exception is that you are limited to 2 days in your country of residence (Italy I assume)
Please note that Portugal is very hard to reach by train : from Geneva you'd need 2 full days (10h+) with an overnight in either San Sebastian or Madrid.
One route is via Madrid and Badajoz (more for Lisbon) or via Vigo (best one for Porto). If I were you, I'd take both :)
Reservations for Spanish trains (pretty much all of them need one) can be made in Spain, Germany or Switzerland (not online).
The TGV into Spain is very popular and some summer dates are already sold out (27-37€ seat reservation). Alternative : reservation-free coastal route via Portbou
RENFE is due to restart the direct train between Lyon and Barcelona in July. It would be very useful to you. However we don't know whether Interrail will be accepted or not and at which cost.
Some info about Madrid - Portugal : https://www.seat61.com/trains-and-routes/madrid-to-lisbon-by-train.htm
https://www.seat61.com/international-trains/trains-from-Madrid.htm#Spain-Porto
Seat61 is also very helpful in general.