Proton-induced quasifree knockout reactions provide a powerful probe of nuclear single-particle structure and reaction dynamics in both stable and neutron-rich nuclei. In this work we develop a unified theoretical framework for the calculation of inclusive $(p,2p)$ and sequential $(p,3p)$ reaction cross sections and fragment momentum distributions at intermediate and relativistic energies. The approach is based on a probabilistic extension of Glauber multiple-scattering theory combined with microscopic nuclear densities obtained from Hartree-Fock-Bogoliubov calculations using Skyrme energy-density functionals. We focus in particular on the sensitivity of total cross sections and longitudinal momentum dispersions to neutron-skin thickness along isotopic chains. Our results indicate that both $(p,2p)$ and $(p,3p)$ reactions exhibit a systematic decrease of cross section and momentum width with increasing neutron excess, reflecting enhanced attenuation and surface bias induced by neutron skins. The effect is significantly stronger for two-proton removal, suggesting that $(p,3p)$ reactions may offer enhanced sensitivity to isovector nuclear structure. These findings establish proton-induced knockout reactions as complementary hadronic probes of neutron skins and the density dependence of the nuclear symmetry energy.

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• Direct reactions
• Knockout reactions
• Neutron skin thickness
• Nuclear fragmentation
• Nuclear reactions
• Nucleon distribution