Microfluidic sorting of synthetic and biological microparticles has attracted much interest in recent years. Inertial microfluidics uses hydrodynamic forces to manipulate migration of such microparticles in microfluidic channels to achieve passive sorting based on size with high throughput. However, most inertial microfluidic devices are only capable of bimodal separation with a single cutoff diameter and a well-defined size difference. These limitations inhibit efficient separation of real-world samples that often include heterogeneous mixtures of multiple microparticle components. Our design overcomes these challenges to achieve continuous multimodal sorting of microparticles with high resolution and high tunability of separation cutoff diameters. We demonstrate separations with flexible modulation of the separation bandwidth and the passband location. Our approach offers a number of benefits, including straightforward system design, easily and precisely tuned cutoff diameters, high separation resolution, and high throughput. Ultimately, the unique multimodal separation functionality significantly broadens applications of inertial microfluidics in sorting of complex microparticle samples.