Electron–hole plasma in two-dimensional systems has mainly been studied in two limiting cases: degenerate semimetals with parabolic bands and nondegenerate symmetric Dirac systems such as graphene. Here we investigate a different regime realized in a gapless HgTe quantum well: a multicomponent plasma where massless Dirac carriers coexist with thermally activated heavy holes from lateral valence-band valleys. Near charge neutrality, the resistance increases approximately as T², in sharp contrast to the nearly temperature-independent resistivity expected for a symmetric Dirac plasma. We show that once heavy holes are populated, charge neutrality pins the chemical potential above the Dirac point, leaving the Dirac electrons moderately degenerate while the heavy holes remain nondegenerate and obey Boltzmann statistics. The light electrons therefore scatter almost elastically from the heavy holes, allowing a relaxation-time treatment of interparticle transport. Using carrier densities from self-consistent band-structure calculations, we reproduce the data with a short-range electron–hole interaction in the weakly disordered limit, for which the conductivity scales as T⁻² and the excess resistivity is proportional to the heavy-hole density. In contrast, an unscreened Coulomb interaction would give a temperature-independent conductivity. The extracted interaction amplitude is of the expected Coulomb scale. These results establish near-critical HgTe quantum wells as a platform for interaction-driven transport in multicomponent systems combining degenerate massless and nondegenerate massive carriers.