According to <G19> from the game manual, the number of balls you can have is only limited to 2 while you are hanging.
<G19> Ball control is limited while Hanging. Robots which are not contacting the Floor may control a maximum of two (2) Balls.
In the context of this rule, “control” implies that the Robot is manipulating the Balls, not simply touching them. For example, if a Ball moves with the Robot either vertically or while turning, then the Robot is “controlling” the Ball. Other synonyms for “control” could be “hold”, “possess”, “support”, “lift”, or “carry”.
There is no restriction on the number of Balls a Robot may control at any other point during the Match. However, a Robot which is controlling more than two (2) Balls must remove any excess Balls from their Robot before leaving contact with the Floor.
Minor, momentary, or incidental violations of this rule that do not affect the Match will result in a warning. Score affecting offenses will result in a Disqualification. Teams that receive multiple warnings may also receive a Disqualification at the Head Referee’s discretion.