Nanoelectromechanical systems (NEMS) have emerged as a promising technology for performing the mass spectrometry of large biomolecules and nanoparticles. As nanoscale objects land on NEMS sensors one by one, they induce resolvable shifts in the resonance frequency of the sensor proportional to their weight. The operational regime of NEMS sensors is often limited by the onset of nonlinearity, beyond which the highly sensitive schemes based on frequency tracking by phase-locked loops cannot be readily used. Here, we develop a measurement architecture with which to operate at the nonlinear regime and measure frequency shifts induced by analytes in a rapid and sensitive manner. We used this architecture to individually characterize the mass of gold nanoparticles and verified the results by performing independent measurements of the same nanoparticles based on linear mass sensing. Once the feasibility of the technique is established, we have obtained the mass spectrum of a 20 nm gold nanoparticle sample by individually recording about 500 single-particle events using two modes working sequentially in the nonlinear regime. The technique obtained here can be used for thin nanomechanical structures that possess a limited dynamic range.