The distance your joists can safely cantilever or overhang a drop beam is determined by 3 factors. 1) The size of the joists 2) The type of material the joists are made from. 3) The spacing between joists. Many building departments limit joist cantilevers to 2' or 3' maximums. You may be able to span further with larger joists or by reducing the joist spacing but be prepared to prove your position.
