Quote Originally Posted by Bearded View Post
From https://ffxiv.consolegameswiki.com/wiki/Grand_Company

Upon reaching the rank of Second Lieutenant, granting access to their stock and allowing acquisition of Grand Company-specific minions and Chocobo Bardings. They will also be eligible to change their Grand Company altogether, though doing so will place them at the lowest rank of Private Third Class.

After changing your allegiance, you must wait 15 days before changing again.
The first change is free, but any subsequent changes will cost 50,000 gil.
Upon returning to a Grand Company after a transfer, your previous rank will be restored, allowing you to 'max out' all three Grand Companies if you wish.
To add to this, when you change Grand Companies, your rank and seals in the previous one don't change. Once the 15 days are up, you can change back and be right where you were.