Optical trapping, a cutting-edge methodology, is pivotal for contactlessly controlling and exploring microscopic objects. However, it encounters formidable challenges such as multiparticle trapping, flexible control, and seamless integration. Here, we employ a polarization-modulated multi-foci technique for versatile nanoparticle trapping using multifunctional metasurfaces relying on geometric phase. Numerical simulations demonstrate the generation of two focused spots with orthogonal polarization distributions through our metasurfaces when illuminated with linearly polarized light, with their polarization distributions be interchanged by orthogonally switching the incident polarizations. We extend this design to an array of multi-foci metasurface tweezers modulated by polarization, highlighting the versatility and robustness of our approach. Furthermore, we demonstrate the simultaneous generation of two distinct focusing cylindrical vector beams using a monolayer metasurface, showcasing the two vector beams possess the interchange ability of their polarization distributions. By leveraging the Maxwell stress tensor, we assess the distinct contributions of the focused beams to longitudinal and transverse optical forces on SiO2 spheres, validating diverse trapping and manipulation behaviors for nanoparticles with the proposed metasurface designs. By manipulating the phase states of Sb2S3 nanopillars, binary-switchable optical trapping and manipulation are facilitated for for all proposed metasurface tweezers. Our work underscores the efficacy of polarization-modulation multifunctional metasurface tweezers in consolidating multiple trapping tasks into a single device, paving the way for innovative lab-on-a-chip optical trapping applications in biophysics, nanotechnology, and photonics.