We propose a novel method to measure flavor oscillations and charge-parity ( C P ) violation in charm mixing. The approach applies to multibody charm decays, such as D0 → K0Sπ+π−, and avoids the need for a fit of the decay amplitudes while suppressing biases due to nonuniform signal reconstruction efficiencies as functions of phase space and decay time. Data are partitioned in decay-time and Dalitz-plot regions (bins). The Dalitz-plot bins are symmetric with respect to the principal bisector and chosen to ensure nearly constant values of the strong interaction phases in each. The ratios of signal yields observed in each symmetric bin pair are fit as functions of decay time, using independent auxiliary measurements of the strong interaction phases as constraints, to determine the relevant physics parameters. Simulation shows a 35% improvement in sensitivity to the normalized charm-eigenstate mass difference with respect to existing model-independent methods. In addition, we introduce a parametrization of oscillation and CP-violation effects in charm mixing that has attractive statistical properties and may find wider applicability.