It is possible to link multiple FFXIV service accounts to a single Square Enix ID. After logging in, you will see the game title screen as normal. Selecting "Start" will display a list of active service accounts. You cannot see which characters are on which account until you select one. You can always back out to the game title screen and select a different account. You don't have to log out completely just to switch characters.

You might be able to log on from two systems at once (using the same SQEX ID, but different service accounts,) but I don't know how SE security would view that. I think "account sharing" is against the terms of use.