No disrespect Heavies, but apparently you can.
FlappJackson has changed his Four times and still has multiple active accounts if I’m not mistaken.
Heck, looks like he even gave himself positive feedback on his trader profile:
From Flappjackson’s trader profile:
Good buyer. Smarter then everyone else I've dealt with.
Comment by: mauidog
Mauidog is formerly known as Moosed and DarmokandJaladatTanagra and currently known as FlappJackson.
So it can be done.