at one time?

One + EDI or Rex.

Max you can have 4, and with you it would be a killing party of 5 !!!!!
The first 2 will be your normal companions.
Number 3 : If your NCR reputation is LIKED, you can call upon either a trooper or ranger to help you fight. (if they die in battle just call again for a new trooper/ranger)
Number 4: is located in FREESIDE you can hire a bodyguard for 100 caps at the north or east gate.

So 2 main followers, NCR trooper/ranger, Freeside bodyguard and YOU makes for an incredible FIVESOME.

I still hope there is a glitch somewhere to allow me to pick two companions. (I don't want Rex or ED-E they're both awful, I want human companions, plural)