Processes leading to a final state with at least two high transverse momentum leptons (electrons or muons) are studied using the full e±p data sample collected by the H1 experiment at HERA. The data correspond to an integrated luminosity of 463 pb−1. Di-lepton and tri-lepton event classes are investigated. Cross sections of the production of e+e− and μ+μ− pairs are derived in a restricted phase space dominated by photon–photon collisions. In general, good agreement is found with Standard Model predictions. Events are observed with a total scalar sum of lepton transverse momenta above 100 GeV where the Standard Model expectation is low. In this region, combining di-lepton and tri-lepton classes, five events are observed in e+p collisions, compared to a Standard Model expectation of 0.96±0.12, while no such event is observed in e−p data for 0.64±0.09 expected.