In the past in Geneva it hasn't been possible to apply for more than one place with a given Regie at a given time. This may however have loosened up due to the ridiculous pressure on the market right now.
I would suggest consulting with
ASLOCA before during and after any tenancy in Geneva.
Better yet if you can afford to hire a lawyer to take care of the application process for you then you stand a much better chance of surviving the process with your emotional health intact.
-mark