Scaling the current tension in the anomalous magnetic moment of the muon with the square of the lepton mass ratio, as predicted by minimal flavor violation, suggests that the analog quantity for the τ lepton, aτ, could be affected by physics beyond the Standard Model (BSM) at the level of 10−6, and even larger effects are possible in generic BSM scenarios such as leptoquarks. While present limits are too weak to even probe the Schwinger term, the situation can improve significantly with e+e−→τ+τ− data from Belle II assuming the SuperKEKB e+e− collider is upgraded with a polarized e− beam. We study what it would take to become sensitive to realistic BSM contributions, one prerequisite being two-loop accuracy in the Pauli form factor F2. We conclude that the most promising avenue would proceed via a combined analysis of transverse and longitudinal asymmetries in e+e−→τ+τ−, requiring and further motivating a SuperKEKB upgrade with polarized electrons.