Simultaneously measuring multiple eigenmode frequencies of nanomechanical resonators can determine the position and mass of surface-adsorbed proteins, and could ultimately reveal the mass tomography of nanoscale analytes. However, existing measurement techniques are slow (<1 Hz bandwidth), limiting throughput and preventing use with resonators generating fast transient signals. Here we develop a general platform for independently and simultaneously oscillating multiple modes of mechanical resonators, enabling frequency measurements that can precisely track fast transient signals within a user-defined bandwidth that exceeds 500 Hz. We use this enhanced bandwidth to resolve signals from multiple nanoparticles flowing simultaneously through a suspended nanochannel resonator and show that four resonant modes are sufficient for determining their individual position and mass with an accuracy near 150 nm and 40 attograms throughout their 150-ms transit. We envision that our method can be readily extended to other systems to increase bandwidth, number of modes, or number of resonators.