I agree with Clif on the power. Heartland's been putting 3 A/C units into toy haulers for a while. They are currently shipping with a Power Control System, but used to just have a switch that allowed you to run only 2 at a time. That was a limitation when running on generator power where you have around 5500 watts of power. On 50 amp shore power, you'll have 12,000 watts.
Apart from whether there's enough power, there would be some challenges.
- You may have to rearrange the loads in your circuit breaker panel to balance things out. If you have too much on one power leg, you'll trip breakers.
- Roof mounting may be problematic unless your coach's roof already has the cutouts and bracing for an A/C unit. And if the 3rd A/C unit wasn't offered as a factory option, the roof is likely not prepped.
- If you have a laminated roof structure, running power may be difficult.
- Tying into the existing ducts could get good results - or not. There's some engineering work that goes into duct size and placement. Unless your rig had an option for a 3rd factory installed unit, dropping a 3rd A/C unit into the mix probably wasn't part of the engineering work that was done.