How can I soundproof an interior door?
Hollow core doors are actually not totally hollow, they typically have cardboard glued inside which just serves to stop the panels from warping.




Sound moves through both air and structure. 



Your main concern should be air - are the doors totally sealed, especially the gap at the bottom? The door should shut tight, and ideally be air-tight. 

You should also consider vents joining the rooms, as sound can travel there as well. On the flip-side, you do need vents in the room (both a way in and out), or the air will get stale, it won't be heated/cooled, and worst case can actually lead to mold growth. It is only fairly recently that they started building homes with return vents in most rooms -- in older homes, the gap under the door is actually the only way air circulates when the door is closed, and usually there is just one return vent per floor.



You can only minimize sound travelling through structure. Using a foam core door or an interior door designed for soundproofing would be a good option. A solid door should also transmit less sound than a hollow one. An exterior door may also be an option. 

There are of course other concerns like sound travelling through walls and other structure, but that's beyond the scope of this question and also fairly well covered by other questions.