I know of no rule limiting how many picks a team can have. There is the Stepien rule, but that's about not having picks in consecutive years.
Hope Resurrected: "I think I can bring an attitude to a team as far as, ‘All right, no matter what, we are not losing this game'." - Kemba Walker
"Its okay to be bad; just so long as you're bad ass." - Keetch
"I don't care if he uses a sophisticated pulley and tackle system to get his shot off if the bitch goes in."-Mustachio
I may be going off of an old memory that is incorrect. Google search doesn't show any limit. Not sure if I can ever remember a team having 4 picks in the 1st round but it may have happened.
Tyrus Thomas and Diaw, Corey Maggete for Blatche, Rashard lewis and their 1st round draft pick?