Warfare & Tactics

Possible? Sure, but it can be difficult depending on circumstances, if your whole corp for example has good Galllente standing, it wouldn't be hard for every person to roll one alt and put them in Caldari, run a few plexes get a few promotions and offset that Gallente standing with the Caldari characters in the corp....

The difficult part comes in though, that as the formerly Gallente corp joins Caldari, they will start getting promotions and whatnot when they get plexes, meaning that if they then want to switch back to Gallente they will have to roll totally new alts and repeat the process, moreover their Gallente peers aren't likely to welcome them back with open arms. I remember Winmatar. immediately getting wardecced last time they joined Minmatar for example, so it works pretty well to switch from one faction to an opposing one once, but to do so more than once makes people pretty nervous about working with you or potentially even hostile.

That being said, switch between Minmatar/Galente or Amarr/Caldari all you want, there are no consequences and no one really cares too much when that happens. The difficulty is only in switching from opposing factions.

So possible? Yes. Good idea? Depends on what you want to accomplish and the circumstances involved. If you hate the leaders of your current milita and want to be friends with your current enemies, then great, just don't swap again after that. If you want to farm LP, then just wait for the pendulum to swing.

You should switch to Minmatar and then not switch back. Only sensible choice TBH.