  The quantum off-shell recursion provides an efficient and universal
computational tool for loop-level scattering amplitudes. In this work, we
present a new comprehensive computational framework based on the quantum
off-shell recursion for binary black hole systems. Using the quantum
perturbiner method, we derive the recursions and solve them explicitly up to
two-loop order. We develop a power-counting prescription that enables the
straightforward separation of classical diagrams. We also devise a
classification scheme that optimizes the integration by parts (IBP) reduction
process, which makes higher-loop calculations more tractable. By employing the
soft expansion technique, we remove irrelevant terms from the loop integrands
and express them in terms of master integrals. We classify the one-loop and the
two-loop classical diagrams, and their loop integrands are represented by
linear combinations of the master integrals. Finally, we explicitly calculate
the classical scalar 2 to 2 amplitudes in the potential region up to the 3PM
order and reproduce the known results.
