The Standard Model (SM) is characterized by a well-defined pattern of couplings of the gauge bosons to the fermions. Any deviation from this description would correspond to a definitive hint for beyond SM physics. These deviations would manifest in terms of different yields for the final states in a direct search. In this letter, we develop a universal framework to extract the extent to which a direct search can probe these differences. Our strategy is effectively demonstrated for a heavy neutral $Z$ decaying into a pair of electrons and muons with different branching fractions. We note the implications of the drastically different reconstructions (especially in the HL-LHC) on the computation of discovery significance as well as the extraction of non-universality. The potential of the current and future $pp$ colliders, quantifying the extent of the asymmetry (in yields) to which they are sensitive, is explored. While the HL-LHC phase offers an optimistic but a restricted picture, it naturally paves the way for the FCC-hh machine. The latter being sensitive not only to heavier masses but also to minor departures from universality in the couplings for the lighter masses.
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