A search for new physics using three-lepton (trilepton) data collected with the CDF II detector and corresponding to an integrated luminosity of 976 pb−1 is presented. The standard model predicts a low rate of trilepton events, which makes some supersymmetric processes, such as chargino-neutralino production, measurable in this channel. The μμ+ℓ signature is investigated, where ℓ is an electron or a muon, with the additional requirement of large missing transverse energy. In this analysis, the lepton transverse momenta with respect to the beam direction (pT) are as low as 5  GeV/c, a selection that improves the sensitivity to particles that are light as well as to ones that result in leptonically decaying tau leptons. At the same time, this low-pT selection presents additional challenges due to the non-negligible heavy-quark background at low lepton momenta. This background is measured with an innovative technique using experimental data. Several dimuon and trilepton control regions are investigated, and good agreement between experimental results and standard-model predictions is observed. In the signal region, we observe one three-muon event and expect 0.4±0.1 μμ+ℓ events from standard-model processes.