Is it possible to progressively apply multiple Stabilization treatments to a single clip. I.e. Using different stabilization methods to progressively improve that stabilization of shaky footage?
The workflow would be to trim the clip to only the part used in the final edit, pre-compose moving all attributes to the new comp and trimming the new comp to the length of the layer, and naming the new comp something like First Pass. In the Main comp, you would run Warp Stabilizer on the First Pass layer, your nested pre-comp.
When that has been completed, a few things will happen to the clip. It will be scaled up and warped to try and mitigate camera movement. You can then Pre-compose again, naming the new comp "Second Pass," and run Warp Stabilizer again. The clip will be warped some more and scaled up again. You might be able to gain a little smoothness, but you will lose quality, and the warping will be increased. You will quickly move into an area of diminishing returns. I have had to use other stabilization workflows on many shots because the distortion was unacceptable. It all depends on the shot. I have never felt the need to run Warp Stabilizer more than once. There are a lot of parameters that you can adjust to try and mitigate distortion and scaling.
If you are doing a composite, like a screen replacement or adding a graphic to something in the background, you need to do the compositing before you run Warp Stabilizer the first time; then you need to select all layers, pre-compose, and run Warp Stabilizer on the pre-comp so that the composited elements get distorted in the same way that the footage does.
If you need to run camera tracking on the shot, that must be done before you run Warp Stabilizer and Pre-compose. The warping will significantly decrease Camera Tracking accuracy and could cause it to fail completely.
A better option may be to motion stabilize the shot by picking some piece of fixed geometry in the shot and using Mocha AE to remove all movement from that part of the shot. You can then add your composites, parent everything to a null, then animate the scale, rotation, and position of the null to fill the frame and turn a bad camera move into a better one.
The most efficient workflow depends on the shot. Share the shot, and we can make more meaningful workflow suggestions.