Patrick Chase
I imagine this has been done by David and others, but a previous thread motivated me to do a quickie test of feasible shaving thicknesses with a close-set cap iron.

I first attempted to set the cap iron on a #6 (the plane I had in front of me) 5 mils from the edge. Both the iron and the cap iron edges were straight. Photographic analysis reveals that the actual setback was 5.4 mils, consistent to within +/- -.2 mils from end to end (it's remarkable how uniform you can get it with the "shininess method"). The plane has common pitch, so the cap iron is level with the sole when the edge of the iron takes a shaving with a thickness of 5.7*sin(45) = 3.8 mils.

I then prepared a 1.5" wide by 8" long test specimen of plainsawn curly maple (from a piece that I keep around for the purpose). Because the specimen is narrower than the plane iron I don't have to worry about edge effects, and so cuts with the cap iron edge below the plane sole are feasible.

I started with a 2.0 mil cut and progressively increased the cut depth until the surface quality was noticeably degraded in some way (I don't care about the shaving, for obvious reasons). I also subjectively noted planing forces while doing so. I did this several times to verify that my results were consistent.

The results:

The plane cut easily up to a 3.0 mil cut depth, and planing forces increased moderately from there to 4.0 mil cut depth. Planing forces increased very rapidly above 4.0 mil depth. While I could consistently take a clean 4.5 mil cut with very high effort, I never obtained a clean cut at 5 mils or higher. 5+ mil cuts led to surface "furriness" in some cases, and ridges from my inability to keep the plane moving steadily in others.

Recall that one point of contention in our previous debate was whether it made sense to camber or otherwise do something with the corners of the cap iron to allow the center to be positioned below the sole.

Clearly it is possible to make clean cuts with the iron positioned basically at (4 mil cut) or just below the sole (4.5 mil cut). "Possible" is not the same as "a good idea" though, and I don't think that the 4.5 mil configuration in this test was really usable. The 4 mil configuration was marginally usable, and you would need to do something about the cap iron corners to use that without tracking on any workpiece wider than the iron.

The "sweet spot" in terms of maximized tearout prevention without exorbitant force addition seemed to be at about 3 mil cut depth, at which point the leading edge of the cap iron is nominally 0.8 mil above the plane sole. If the cap iron is truly set level to within 0.8 mil all the way across, then corner engagement would be a non-issue. With that said, I think you can make a fair argument that tapering the corners as Brian does is sensible, if only to be safe of the cap iron ends up tilted a bit.