The DSS or private schools have no contact themselves as expected, so theoretically you can hold "infinite" no. Except once you registered all DSS ad some private schools, you cannot do the second round govt lucky draw. And I know a few even don't allow the first round too!
Of course, holding a lot of schools are not only bad for others, and also for the sake of your child. Personally, I found nowadays K3 kids know a lot already, and most of them are eager to become a P1 kid very soon and really like to know their prospective school. So make your decision early, the kid will be happier to adapt to the new school. And you are also making other families on the waiting list happier.