Is it permissible to hold multiple Friday congregational prayers (Salat al-Jumu'ah) in close proximity, and what is the specified distance between two mosques for holding a second Friday prayer?

The basic principle is that it is not permissible to hold multiple Friday prayers in a single town, unless there is a need, such as the mosque being too small, or too far, or fear of sedition. The criterion for the permissibility of multiple Friday prayers is need, not a specific distance. Friday prayer is obligatory for anyone outside the town who is at a distance of a farsakh or less (more than 5 km) from it. As for the people of the city or town, they are obligated to go to it, even if they are far away.