Optical trapping combined with Raman spectroscopy have opened new possibilities for analyzing biological nanoparticles. Conventional optical tweezers have proven successful for trapping of a single or a few particles. However, the method is slow and cannot be used for the smallest particles. Thus, it is not adapted to analyze a large number of nanoparticles, which is necessary to get statistically valid data. Here, we propose quasi-bound states in the continuum (quasi-BICs) in a silicon nitride (Si3N4) metasurface to trap smaller particles and many simultaneously. The quasi-BIC metasurface contains multiple zones with high field-enhancement ('hotspots') at a wavelength of 785 nm, where a single nanoparticle can be trapped at each hotspot. We numerically investigate the optical trapping of a type of biological nanoparticles, namely extracellular vesicles (EVs), and study how their presence influences the resonance behavior of the quasi-BIC. It is found that perturbation theory and a semi-analytical expression give good estimates for the resonance wavelength and minimum of the potential well, as a function of the particle radius. This wavelength is slightly shifted relative to the resonance of the metasurface without trapped particles. The simulations show that the Q-factor can be increased by using a thin metasurface. The thickness of the layer and the asymmetry of the unit cell can thus be used to get a high Q-factor. Our findings show the tight fabrication tolerances necessary to make the metasurface. If these can be overcome, the proposed metasurface can be used for a lab-on-a-chip for mass-analysis of biological nanoparticles.