If you want to output the Remove and Stabilize modules, you would need to have 2 instances of the plug-in as you are right: you can only render one module at a time.
However, you would be able to use the same Mocha plug-in instance for many tasks. You could output the Remove Module render and also export the tracking data from the same project and copy it as keyframe data.
You may want to explore using the stabilize module and exporting stabilized tracking data in the AE format, pasting back to AE. Another option is the regular tracking data can also be "inverted" on export.
Hope this helps. If you are applying multiple instances of the plug-in on 1 clip, you might want to precomp in-between.