If I understand you correctly, you have an existing dual sink setup with a double wye or perhaps a double tee (dwv), and you want to add in a why or tee (dwv) to add in a sink sink on the other side of the wall in a new bathroom.
If you do this, you will make all three sinks a wet vent installation. You say you have a 2" stack to work with, and if your code allows that many fixture units on a 2" stack, then it should be fine to do so. Now if your dual sinks are already plumbed, it would be easier to add in the wye or tee (dwv) underneath the double wye or double tee (dwv) so that you don't end up placing the new p-trap too high.
Another option would be to simply to cut out and reverse on of the 90s on one of the trap arms that you have and turn it around and point it out backwards for the new lav sink, then use the remaining trap arm in the existing bathroom to drain both sinks from a single p-trap....like you would for a kitchen sink.