This can be done, but not as interlocking or real time as everyone thinking. It's designed around "points". Factory (or maybe materials) points, health / hospitality points, etc.

Basically you'll be given some "special" buildings where you can place the other-genre games . Let's say that you have a "60x60 1 level hospital" that when you placed it in the city, you can interact with it via theme hospital style.

Now in theme hospital-like, it has reputation / ratings where it translate directly to "hospitality points" for your city. When you exit the mode, it stopped the simulation and the points freeze. Similar with factory points.