I was actually able to do a surprising amount with a hollow door the other day. I'm replacing the door that comes into the studio from the stairwell with a solid core door, and I moved the hollow door to the laundry area which is not mission critical to any kind of soundproofing. But just as a test, I wanted to see just how well this door would do at "soundproofing" the laundry room. I remember reading in Acoustics 101 that it's not totally the door itself that lets sound through, but mostly the perimeter around the jamb and at the bottom. So after I moved this door back to the laundry area I caulked around the jamb first to seal that up. Then I used some closed cell weather stripping all around where the door actually meets the jamb. On the hing side I put the weather stripping where the side of the door closes. The bottom of the door is rubbing pretty badly on the carpet, so I let that be. This area is always loud because it has the laundry, furnace, and hot water heater. After I treated the door with just a couple simple methods, I was seriously surprised at how much sound it actually stopped.
Now, I'm not necessarily recommending that you keep the hollow core door, I just wanted to illustrate how much treating the edges of the door will help stop sound.