Use one keyfob for two system (different houses)?

We have a SimpliSafe system for our house. Our son, who lives a few miles away, also has one. An idea just crossed my mind... can I register my keyfob at HIS house, so that I can control his system with my keyfob? Of course, I mean that I want my keyfob to continue to work with my system, and IN ADDITION to work with his system too. (Then, we would register his keyfob with our system, so he can control both systems from one keyfob too.)

What I have in mind is the way remote garage door openers can be programmed for more than one garage door. Would something similar work with the keyfob? I know I could just go ahead and try, but I'm not sure if that might screw something up. Thank you!