You can have as many as your computer can handle logged in as long as the server player count is under a certain number.
Edit: Well on second glance, the Code of Conduct says if there are 1500 or less folks on a shard, you're limited to 3 accounts. It doesn't scale down either, which seems strange. There's like 150 people on Reunion at the time of this posting, but with the CoC in mind, that means only 3 accounts logged in at once as the cap. Oh well, I'll play by their rules, I'm happy to play at all.