  Neutron star mergers are very violent events involving extreme physical
processes: dynamic, strong-field gravity, large magnetic field, very hot, dense
matter, and the copious production of neutrinos. Accurate modeling of such a
system and its associated multi-messenger signals, such as gravitational waves,
short gamma ray burst, and kilonova, requires the inclusion of all these
processes, and is increasingly important in light of advancements in
multi-messenger astronomy generally, and in gravitational wave astronomy in
particular (such as the development of third-generation detectors). Several
general relativistic codes have been incorporating some of these elements with
different levels of realism. Here, we extend our code MHDuet, which can perform
large eddy simulations of magnetohydrodynamics to help capture the magnetic
field amplification during the merger, and to allow for realistic equations of
state and neutrino cooling via a leakage scheme. We perform several tests
involving isolated and binary neutron stars demonstrating the accuracy of the
code.
