  Faster likelihood evaluation enhances the efficiency of gravitational wave
signal analysis. We present Mode-by-mode Relative Binning (MRB), a new method
designed for obtaining fast and accurate likelihoods for advanced waveform
models that include spin-orbit precession effects and multiple radiation
harmonics from compact binary coalescence. Leveraging the "twisting-up"
procedure of constructing precessing waveform modes from non-precessing ones,
the new method mitigates degrade of relative binning accuracy due to
interference from superimposed modes. Additionally, we supplement algorithms
for optimizing the choice of frequency bins specific to any given strain signal
under analysis. Using the new method, we are able to evaluate the likelihood
with up to an order of magnitude reduction in the number of waveform model
calls per frequency compared to the previously used relative binning scheme,
and achieve better likelihood accuracy than is sufficient for obtaining source
parameter posterior distributions that are indistinguishable from the exact
ones.
