I've considered that approach, but that means keeping the code fully retrocompatible, and that kinda leads to madness :D

Plus if you have different processes per client, you can provide better security, particularly in terms of leaking customer data to each other. In our case, we just used different Linux and Postgres users for each client, but even just that meant that a few security bugs discovered in the application couldn't be used to read/write data of other customers.