@Ethan Blue
So many people have posted and I haven't read them all but here is my experience that I just went through with shared furnaces. We purchased two foreclosed units in a small town- two tri-plexes. When we went to go turn the water on we learned that we needed them inspected before we could rent them out- no problem. The town nor the inspector had a list of what was need to pass inspection but one of the things was the shared furnace. We called the Wisconsin state inspector and he informed us that nothing is wrong with a shared furnace but it just needs to be separate cold air returns such as a common hallway it could not pull from inside a unit.
Here is my two sense: find out if there is a pre-inspection from a city official! That being said if we had decided to put in separate air returns we would have put a lock on thermostat that controls the unit ( the plastic cover kind) and leave it set at 69 degrees.
We opted to instead close the furnace off to the other units let it heat one ( it was not large enough to heat all the units) and install small wall natural gas heaters which were about 1200 a piece. This allows tenants to control their own heat and also to pay for their own heat!