ABSTRACT Fundamental cosmology observations, such as the detection of the redshift drift and tests of the universality of physical laws, are key science and design drivers of the ArmazoNes high Dispersion Echelle Spectrograph (ANDES), an Extremely Large Telescope instrument. While separate forecasts for each of them have been reported, we have developed Fisher matrix based forecast tools combining both of these observables. We demonstrate the synergies between the two ANDES data sets, quantifying the improvements in cosmology and fundamental physics parameter constraints for two separate theoretical paradigms. We publicly release this forecast code, which is one of the tools for the optimization of the ANDES observing strategy.