Manipulation of submicrometer particles in Lab-on-a-Chip systems using acoustophoresis is challenging due to the effect of acoustic streaming. We numerically study the transition from radiation force dominated to streaming-induced drag force dominated acoustophoresis using the fundamental and higher-order resonances of a water-filled rectangular microchannel. We consider the cases of single mode excitation and simultaneous double mode excitation. The acoustic fields at resonance are calculated using a second-order perturbation expansion of the thermoviscous acoustic problem. We show that the acoustophoretic forces using simultaneous mode excitation can be obtained from a linear combination of the single mode forces. We find that the critical size of suspended particles at the transition scales inversely with the square root of the resonance frequency. Particle tracing shows radiation-dominated concentration of 800 nm diameter polystyrene particles using the fifth-order resonance at 9.8 MHz. For smaller particles we find a streaming-assisted concentration regime where particles are concentrated into the streaming regions close to the walls. In case of double mode excitation, the particle concentrations increase a factor 4 to 18 times for 200 nm to 800 nm particles respectively. We include the numerical model, consisting of a COMSOL implementation and MATLAB control script, as supplemental material.