You can upgrade your phone anytime you want.

If I have 3 phones on my account can I upgrade all 3 at the same time or do I have to only do 1 and then do the others at a later time.

If you want to upgrade through EIP.  The answer can vary.  Customer Care at 611 or by reaching out to T-Mobile via DM on Facebook or Twitter will get you someone that can look at your account and tell you what your options are.  

chances are they will not let you upgrade right away IF you already have an EIP or a lease.  If they do they’d probably make an exception if 50% of the device has been paid.

It all depends on how long you've been with Tmobile and credit. I have 2 active EIP’s on my line and I'm still able to upgrade if I want to a 3rdb phone on my line.