Yes, I feel that Rome and Paris should open the door to allowing each other to have more twin cities. Many other places have twin cities, or sister cities, with numerous locations. For example, Portland, Oregon has ties with Sapporo in Japan, Guadalajara in Mexico, Mature in Zimbabwe, and several other international cities. You don't have to be restricted to just one twin city!
Twin cities are something that looks nice on the "Welcome to X" sign, but really count to nothing else except the occasional ceremony and exchange. No one really cares about the idea of twin cities, so even if somewhere wishes to be twinned with everywhere on the map, why not let them?
No, Paris and Rome should remain the only twin cities for each other. Both Paris and Rome have no equal besides each other as far as culture, history and beauty are concerned. If other cities would like to become twin cities with either Paris or Rome, they should look elsewhere.
When you fly into Chicago and get on the L, there is a long list of cities that are sister cities with Chicago. There are so many that no one would ever learn then or be able to keep them straight. It is better to have only one twin city so that people can learn about it and appreciate it.