Just saw your posting, and was not sure if you would see my response since your post is several weeks old.
Most, if not all code restrictions would not allow for two fireplaces, stoves, or other wood-burning appliances to share a common chimney. This is because one of these units, when lit, could cause carbon monoxide to be expelled out the other. I know, for example, that gas-fired central heaters and hot-water tanks can share the same flu, but that, I believe, is due the cleaner-burning nature of the fuel.
At any rate, you will need, I'm sure, another chimney for the second stove, and there may be requirements for how close one can be to the another chimney, or that one has to be taller than the other so the smoke of the one lit does not get sucked down the one that is not lit. Besides the danger of CO2, there is also the danger of fire from a misrouted spark. If codes were not followed and permits not issued, a fire in your house may not be covered by your insurance.
Installing another chimney is really straightforward, however, especially with the stainless steel sections. I've done quite a few, and found them easy to work with. Just remember that when dealing with fire, adherence to the rules is the only way. Check with your municipality to see what you need to do.