whats the maximum number the game allows without glitching?

You are limited to a maximum 2: these are dependant on the species: you can only have 1 robotic: ED-E or Rex; and 1 Human companion at any time. So you can have Boone and ED-E; Rex and Cass; but not Cass and Boone or Rex and ED-E.

You can increase this by getting a Ranger with the Emergency Radio, and there are other bonuses you can obtain.

Reno

can I have veronica and boone?

Nope, as both are human or at least humanoid.

As has been stated you can have one humanoid and one animal/robot companion following you at the same time, although there are some quest followers, the summonable factional minion and in one specific small area a hireable bodyguard (but they only stay within that specific area and don't follow you out of it).