Adding devices makes I2C read 0 I'm using an Arduino Due with a logic level converter to interface with two different 5v sensors via I2C. Being of poor quality, these sensors have no data sheet. 

When either one of these sensors is plugged in, I am able to read from it without issue. The moment I plug the other one in as well, the I2C stops working, and I just get 0. I know that it's not an address collision issue, because they have different addresses.

I tried adding an additional set of pull-up resistors (such that they are in parallel with the built-in ones) in order to counteract potentially increased bus capacitance, but no dice.

What could be causing this issue? I apologise for asking such a noob question.
Your problem is probably from the level converter. Which one did you use?
Most level converters are uni-directional, and don't work for I2C.
See the App note and device from NXP:
http://www.adafruit.com/datasheets/an97055.pdf