As long as you have both wheels on each side going in the same direction with the same speed, it works like it normally would, no changes.
Strafing, however, would not be permissible with all 4 modes: you would have to use strictly torque/speed on the strafing motion.
I don’t see how it would work with either mode. If you have the ring gear adding speed to both of them when going forward it will work but if you reverse one wheel the ring gear will now subtract speed (thereby adding torque) from the one that is reversed. The same will happen if you are in the other mode to begin with.
I see this same problem as well.
In order to strafe, the front and rear motors must be going in opposite directions, which means that in whatever direction the third motor is going, it will make one side wheel go high-torque and the other go high-speed.
If you didn’t use the third motor for strafing, then it would work, but then you only have 4 motors to strafe with.
When the side is uniform, all 3 motors (both rings and the common carrier) turn.
When the side is not uniform (i.e strafing, both wheels opposite directions), the motor controlling the carrier gears simply would not turn.
https://vexforum.com/gallery/files/4/1/6/3/0/8/planets.jpg
This is a mock-up of my proposed gearing.
Replace Traction Wheels with mecanums (my diagram’s axles are too short and the view was obstructed).
Middle motor turns only if both wheels are turning in the same direction at the same speed. It would not turn if strafing (opposite directions).
I would have made the wheels further apart by having the center motor use the chain and the ones at the front and back directly driving the planet carriers.
But awesome CAD 
You still have the same backdriving issue as I explained in the 4194B thread, so you’ll need to put a lock in somewhere.
Eh, it’s a mock-up. I would definately relocate those driven sprockets, and would probably use some chain on the carrier gear system; I was just making a demonstration.
Thanks 
Yeah, I’m thinking about the backdriving issue as well. I’m pushing to get some pneumatics from the club to at least experiment with for the summer (we have to maintain 5 ‘equal teams’ and we only have 1 or 2 sets).
Also I think you would want to gear down the center motor (for torque) as it’s exerting force on both the front and the back (so needs twice the torque to maintain the force balance on the planets), but it might work either way.
Only six motors would be required for a mecanum wheel drive, follow the CAD model however drive the planet carriers of each planetary, then chain the entire thing to a single motor in high torque configuration with more emphasis on torque since it will have to fight two motors. This will actually allow for speed mode in torque mode, whilst allowing for strafing since the two planetaries would be able to operate independently when the third motor holds the chain still. I’m actually constructing a prototype as of this second. Hopefully I can get it working by the end of this week.