Tile over old uneven tile floor?

[Joe Edwards-Hoff]

So, I've got to rehab my first apartment unit. The building is from 1945 and it may have the original tile floor in the shower. It is uneven and ugly. I'm not sure how easy I can rip things up. Can I level it out (with correct slope)  and then just tile above it? Extending the drain some... I'd buy a drop in pan if I could but it is 30x30 with a drain that isn't centered.  So I assume I'm out of luck there. 

The walls will get torn out today.