Microfluidic particle and cell manipulation techniques possess many potentials for biomedicine and healthcare. Many techniques have been developed based on active (e.g., electrical, magnetic, acoustic, and thermal) force fields and passive hydrodynamic forces (e.g., inertial and elastic lift forces). However, techniques based on a single active or passive manipulating physics cannot always meet the demands, and combining multiple physics becomes a promising strategy to promote technique flexibility and versatility. In this work, we explored the physical coupling of magnetophoresis with the elastic and inertial (i.e., elasto-inertial) lift forces for the manipulation of microparticles. Particle lateral migration was studied in a coflowing configuration of viscoelastic ferrofluid/water (sample/sheath). The particles were suspended in the viscoelastic ferrofluid and confined near the channel sidewall by a sheath flow. The coordination of magnetophoresis and elasto-inertial lift forces promoted the cross-stream migration of particles. Besides, we investigated the effect of the flow rate ratio and total flow rate on the migration of particles. Furthermore, we also investigated the effects of fluid elasticity in sample and sheath flows on particle migration using different combinations of sample and sheath flows, including Newtonian ferrofluid/water, Newtonian ferrofluid/viscoelastic fluid, and viscoelastic ferrofluid/viscoelastic coflows. Experimental results demonstrated and ascertained the promoted particle lateral migration in the PEO-based ferrofluid/water coflow. Finally, we demonstrate the proof-of-concept application of the physical coupling strategy for cell cross-stream migration and solution exchange. We envisage that this novel multiphysical coupling scheme has great potential for the flexible and versatile manipulation of microparticles and cells.