“… lay it flat …” I want to thin (behind the edge) Not the thickness of the entire blade.
You lost me when you spoke of cutting a new relief bevel in the knife. ??
These are related concepts.
Note that most blades do not have a fully flat grind from (just behind) the edge to the spine.
Some knives are flat part way up the blade face (in fact, these are often very slightly concave because they are usually ground on a large radius circular stone). These knives are often wide- bevelled knives. The blade face above the wide bevel is usually pretty flat (but not quite flat enough to be polished on a stone, unfortunately).
Some knives have a convex grind. Once again, this is often in the bottom part of the blade face, with the part closer to the spine being pretty flat. These knives can be wide-bevelled but often are not. Other knives have a concave grind or even a compound grind such as an s-grind.
Let's take the example of a flat ground wide bevel with the wide bevel forming a 3 degree relief bevel. if you "thin behind the edge" at an angle greater than than the wide bevel's angle (say, 7 degrees), you will be cutting a new 7 degree bevel in between the wide bevel and the edge bevel. This is pretty much the same as "knocking the shoulders off" the bevel. It will likely improve performance if the knife has become thick behind the edge but it won't maintain the knife's original geometry, so how it performs in food will change somewhat.
If you want to maintain the knife's original geometry, you want to remove metal evenly from the whole wide bevel until just before the wide bevel reaches a zero grind.
I have used a flat ground wide bevel as the example here because it is the simplest to understand. However the principal is the same for other grinds: if you want to maintain the original geometry, you must remove metal evenly from the whole relief bevel (blade road). This will obviously require some kind of refinishing afterward for some blades. For convex blades, this requires a kind of modified hamiguriba sharpening. For concave blades, it's difficult to maintain the concavity in home use, so they gradually become flat grinds. Compound grinds are difficult to maintain in this fashion.
As for "laying the blade flat" on the stone, what I mean is that if you lay the blade flat on the stone, then place pressure just above the edge, the blade will realign so that the relief bevel (wide bevel in the example of our flat ground wide bevel) is flat on the stone and steel will be removed from the relief bevel only (and not above it).
The technique for a convex blade is a little more complex but still in involves laying the blade flat on the stone.
You certainly can maintain a knife by knocking the shoulders off at, say, 7 degrees per side and it will almost certainly improve performance over not thinning the knife. However, it will gradually change the geometry of the knife.