Wireless Bike computer--can I use 2 of the same model and have 1 sensor feed both?

So I'm having my 1996 Cannondale tandem overhauled, and am removing the defective wired computers and want to run wireless.

First question -- can I buy two computers of the same model, can I use one sensor and have it feed both computers, one for the captain, and one for the stoker? I'm going to guess no, otherwise anytime on group rides there would be interference from other riders.

Which leads to my second question, will two wireless sensors of the same or different brand conflict with one another? I already have a Cateye Strada Slim wireless computer I took off a road bike I can use on the tandem for the stoker, so if I buy another computer, say Cateye Padrone Plus or Planet Bike Protege (has temperature!), will the sensors conflict? I may want a cadence model, so would it work to have both sensors transmitting from the rear wheel?. I just want to make sure having two wireless sensors/computers on the same rear wheel will not cause a conflict.

BTW - its something I want to leave on the bike and not have sync to my phone.