Rules G33 and G34 don’t clarify if the human player is able to introduce more than one ball at a time. I know that robots cannot have possession of >1 ball at a time. Hope there isn’t some explicit rule that I missed in the manual…
from what I saw reading the manual there is very few constraints on the human player because of the separation, but there was nothing that would prevent multiple besides accidentally picking up more than one when you obtain them.