We have a lot of practice running door and window parts at this thickness. In the early days of our euro door building we sometimes mounted 2 feeders on the shaper. It works but is a unhandy setup. We use this shaper for other operations and the second feeder gets in the way especially for curve work.
It depends on how much work you do like this. If a lot of production a 6 wheel feeder is the best solution. Otherwise Jeff has a good solution with support tables. We don't have any issues running thick stiles with a 4 wheel feeder.
Stile cuts usually are not removing a lot of material even at 3 1/2" and you should not have any problems if the work is supported. On deep cuts like euro frame profiles and the outside cuts on deep rebated edges we usually take a glazing bead out here before profiling and that helps a lot. You can also take 2 passes.
But to answer your question more wheels is better for large cuts. Our window machine has a 8 wheel feeder and holds thick parts very secure.
Attached is a video of doing outside profiling on a 92mm door. It is a tricky cut because the whole edge is removed with a split fence. We have had a lot of practice on large frames. Notice the extra support under the extension arm and the glass bead removed on the edges.