We know the theory of general relativity (GR) accounts for the illusive $43$ arc seconds of precession of the perihelion of Mercury. The calculation is well known and well studied. How does one account for the remaining planetary precession? So, more specifically, the effect that the other planets have on the precession of Mercury. I know there are methods listed in the paper by Price and Rush, 1978, which states there is more methods presented in undergraduate mechanics books. However, I have never came across such things.
Is there a method in which one can derive both the planetary and GR precession effects or do we need to separate the precession into a Newtonian and relativistic form and then add them together?
EDIT: Furthermore, what about an arbitrarily chosen planet? The ring method mentioned in the answer by @diracology and the paper that I have linked assumes assumes a uniformly distributed ring of mass surrounding Mercury. However, what if we were concerned with planetary and GR precession effects of Jupiter (just as an example) - Do we then proceed to consider two rings around Jupiter?