Only limited by your settlement caps and resources. Still can only have 1 companion follow you at a time.
That part kind of makes me sad.. I mean, how cool would it be to have two or three of these guys following you around. Also... why can I only have one when it's obvious the Rust Devils can have a multitude following them around. Unfair!
I would have been happy with the follower system from the previous two games: One humanoid and one robot/animal follower. But yea, having a giant sentry and a swarm like bot following you around would have been great, beeps and mechanical noises for all!
You can hack a Sentry bot (not dlc thingie) and then you have 2 bots. Assaultrons (not dlc thinge) something different since they are scripted to attack on sight everyone that is not listed as bot's friends list. You need either a mod / doing some game commands. Assaultrons will not attack any of your companions.
Cheers,
-klevs