Unless all the packs you are trying to charge all start at the some voltage then you could be doing undue damage to the packs. The instant you connect any two packs in parallel current is flowing to bring the lower pack up in voltage and dropping the higher pack. With lipos and a large enough voltage differnece there could be quite a few amps being swapped between the packs. Unless you are running the packs in parallel to begin with so they all end at the same voltage, I would not suggest connecting packs of various discharge levels in parallel.

To actually answer your question, about 4- 5 packs.