Heavy neutrinos (N) remain one of most promising explanations for the origin of neutrinos' tiny masses and large mixing angles. In light of broad advances in understanding and modeling of hadron collisions at large momentum transfers, we revisit the long-standard search strategy for heavy N decaying to multiple charged leptons (), pp → N X → 3 νX. For electroweak and TeV-scale N , we propose a qualitatively new collider analysis premised on a dynamic jet veto and discriminating, on an event-by-event basis, according to the relative amount of hadronic and leptonic activity. We report that the sensitivity to heavy neutrinos at the CERN Large Hadron Collider (LHC) can be improved by roughly an order of magnitude at both L = 300 fb −1 and 3 ab −1. At √ s = 14 TeV with L = 3 ab −1 , we find active-sterile mixing as small as |V N | 2 = 10 −2 (10 −3) [5 × 10 −4 ] can be probed at 95% CL for heavy Dirac neutrinos masses m N 1200 (300) [200] GeV, well beyond the present |V N | 2 10 −3 − 10 −1 constraints for such heavy states set by indirect searches and precision measurements. The improvement holds also for Majorana N , and is largely independent of whether charged lepton flavor is conserved or violated. The analysis, built almost entirely from inclusive, transverse observables, is designed to be robust across increasing collider energies, and hence serves as a basis for searches at future colliders: with L = 15 ab −1 at √ s = 27 TeV, one can probe mixing below |V N | 2 = 10 −2 (10 −3) [2 × 10 −4 ] for m N 3500 (700) [200] GeV. At a hypothetical 100 TeV pp collider with L = 30 ab −1 , one can probe mixing down to 9 × 10 −5 for m N 200 GeV, below 10 −3 for m N 4 TeV, and below 10 −2 for m N 15 TeV. We anticipate these results can be further improved with detector-specific tuning and application of multi-variant / machines learning techniques. To facilitate such investigations, we make publicly available Monte Carlo libraries needed for the precision computations/simulations used in our study.