MUTE (MUon inTensity codE) is a Python program (https://github.com/wjwoodley/mute) that combines two state-of-the-art codes, MCEq and PROPOSAL, to predict muon intensities and spectra in underground and underwater laboratories. Our previous work (A. Fedynitch, W. Woodley, M.-C. Piro 2022 ApJ 928 27) has demonstrated the accuracy of MUTE in reproducing the measured vertical equivalent muon intensities within the models' uncertainties. Moreover, we have shown that the experimental uncertainties are smaller than the theoretical uncertainties, making the vertical-equivalent data an effective calibration source for high-energy neutrino flux calculations. In this new study, we expand our analysis by calculating the total muon intensities and seasonal variations in labs located under flat earth and mountains using topographic maps of the overburdens. While our model predicts the amplitude of seasonal variations well, we identified inconsistencies amongst measurements at several labs, which pose additional challenges for interpretation. Additionally, the uncertainty in the rock density above many labs is a significant source of systematic uncertainty in total muon intensity measurements. Although MUTE accurately describes this data, we found that the uncertainties of the data were similar to our nominal prediction. We also present calculations using the daemonflux model, a muon and neutrino flux model calibrated with muon measurements at the surface, and using constraints from near-horizontal measurements at the highest energies. We examine whether the near-horizontal data is consistent with the underground measurements.