I am not a fan of people being "members" of multiple groups. It gives the impression that player groups are mere communities, not people working together as a unit.
So, my suggestion would be two-fold:
1. Allow the creation of Communities in addition to Squadrons. Canonn, DWx, Fuel Rats, FUC, etc are all examples of entities that perhaps aren't really squadrons, but consists of players from different groups coming together to do things outside of their core group activities. Cmdrs could "pledge" to Communities, just like they can for Minor Factions. Not really sure if there should be a limit to how many communities players can join, but that's probably more of a coding issue than anything else.
2. Allow Squadrons to ally with other Squadrons, not just Minor Factions. This would preferably come with a designated colour code on the scanner for cmdrs in an allied Squadron.
Alternatively a "support" function could be implemented, where you can be a member of one Squadron (which also determines your tags), but can "officially" support one or more other squadrons. Not sure where that would be displayed for other cmdrs though, but a new tab somewhere in the lefthand panel among all the other scan related info would be appropriate.