  As part of the study of the two-body problem in Einstein's gravity, the
fourth post-Newtonian order (4PN) of the two-body effective action is being
computed presently by both effective field theory (EFT) methods and others.
Diagrams with 3 (or 4) classical loops appear to be a significant obstacle. In
this paper we develop a method to compute such 3-loop diagrams and demonstrate
it through a specific diagram. We reduce the classical diagrams through
shrinking the body worldlines to a form more familiar in Quantum Field Theory.
A key ingredient in the evaluation is the Integration By Parts method for
Feynman integrals.
