We perform a detailed comparative study of conventional transverse magneto-optical Kerr effect (T-MOKE) measurements and a methodology that utilizes an effective polarization detection scheme for mixed s- and p-polarized incoming light. To test the ultimate sensitivity of both methods, we also design a series of specialized samples in which the T-MOKE signal of a Co-film is artificially reduced by means of a Ag overcoat of varying thickness. We find that the effective polarization detection scheme leads to a more than 30-fold increase of the T-MOKE signal and signal-to-noise ratio, even under general operation conditions which were not individually optimized. This allowed for the observation of T-MOKE hysteresis loops of Co-films that were buried under 80 nm of Ag, for which the MOKE signal was only 1/600 of that for an uncoated Co-film. In comparison, conventional T-MOKE measurements did not succeed for Ag overcoats thicker than 40 nm.