Not likely! There are a few reasons why that is not feasible. The structural integrity of the entire building would be compromised were the steel reinforced concrete floor/ceiling penetrated to accommodate a staircase between the two units. Fire safety would also be of great concern given the additional threat to life safety due to there being not only the large opening between floors for fire to travel through but the additional life & casualty safety problem of there being two separate electrical panels with two separate main disconnects. Considering the down side I can't envision any sane municipality issuing a permit for such a remodel let alone the Condo association. Have you ever tried to convince an old person to do something that is diametrically opposed their safety and good health? Good Luck!
Gee, I was going to say that I thought it was perfectly feasible. ConMah touches on some important points (construction, fire codes, condo assoc., etc.) but those are all things that can be dealt with. I'd say don't give up on the idea; do some checking around with local authorities.