[en] A search for the decay of the τ lepton to rare multi-pion final states is performed using the BABAR detector at the PEP-II asymmetric-energy e+e- collider. The analysis uses 232 fb-1 of data at center-of-mass energies on or near the Υ(4S) resonance. In the search for the τ- → 3π-2π+2π⁰ν_τ decay, we observe 10 events with an expected background of 6.5^+2.0_-1.4 events. In the absence of a signal, we calculate the decay branching ratio upper limit β(τ- → 3π-2π+2π⁰ν_τ) < 3.4 x 10^-6 at the 90% confidence level. This is more than a factor of 30 improvement over the previously established limit. In addition, we search for the exclusive decay mode τ- → 2ωπ-ν_τ with the further decay of ω → π-π+π⁰. We observe 1 event, expecting 0.4^+1.0_-0.4 background events, and calculate the upper limit βτ-→ 2ωπ-ν_τ < 5.4 x 10^-7 at the 90% confidence level. This is the first upper limit for this mode