  In this paper, we apply the multi-tracer technique to harmonic-space (i.e.\
angular) power spectra with a likelihood-based approach. This goes beyond the
usual Fisher matrix formalism hitherto implemented in forecasts with angular
statistics, opening up a window for future developments and direct application
to available data sets. We also release a fully-operational modified version of
the publicly available code CosmoSIS, where we consistently include all the
add-ons presented in the previous papers of this series. The result is a
modular cosmological parameter estimation suite for angular power spectra of
galaxy number counts, allowing for single and multiple tracers, and including
density fluctuations, redshift-space distortions, and weak lensing
magnification. We demonstrate the improvement on parameter constraints enabled
by the use of multiple tracers on a multi-tracing analysis of luminous red
galaxies and emission line galaxies. We obtain an enhancement of $44\%$ on the
$2\sigma$ upper bound on the sum of neutrino masses. Our code is publicly
available at
https://github.com/ktanidis/Modified_CosmoSIS_for_galaxy_number_count_angular_power_spectra.
