  Massive binaries are vital sources of various transient processes, including
gravitational-wave mergers. However, large uncertainties in the evolution of
massive stars, both physical and numerical, present a major challenge to the
understanding of their binary evolution. In this paper, we upgrade our
interpolation-based stellar evolution code METISSE to include the effects of
mass changes, such as binary mass transfer or wind-driven mass loss, not
already included within the input stellar tracks. METISSE's implementation of
mass loss (applied to tracks without mass loss) shows excellent agreement with
the SSE fitting formulae and with detailed MESA tracks, except in cases where
the mass transfer is too rapid for the star to maintain equilibrium. We use
this updated version of METISSE within the binary population synthesis code BSE
to demonstrate the impact of varying stellar evolution parameters, particularly
core overshooting, on the evolution of a massive (25M$_\odot$ and 15M$_\odot$)
binary system with an orbital period of 1800 days. Depending on the input
tracks, we find that the binary system can form a binary black hole or a black
hole-neutron star system, with primary(secondary) remnant masses ranging
between 4.47(1.36)M$_\odot$ and 12.30(10.89)M$_\odot$, and orbital periods
ranging from 6 days to the binary becoming unbound. Extending this analysis to
a population of isolated binaries uniformly distributed in mass and orbital
period, we show that the input stellar models play an important role in
determining which regions of the binary parameter space can produce compact
binary mergers, paving the way for predictions for current and future
gravitational-wave observatories.
