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A fermionic many-body system with a current mass can be localized within a finite spatial region solely by gravity [1]. Previous studies have investigated systems incorporating electromagnetic fields [2] and their extensions to multiple-shell configurations [3]. In this work, we formulate an Einstein–Dirac–Maxwell system incorporating a Nambu–Jona-Lasinio (NJL)-type four-fermion interaction. We discuss mass generation through spontaneous chiral symmetry breaking in curved spacetime, and report numerical results on the spatial structure and physical properties of self-gravitating many-fermion systems with dynamically generated mass. [1]F. Finster, J. Smoller, S.T. Yau, Particle-like solutions of the Einstein–Dirac equations. Phys. Rev. D 59, 104020 (1999) [2]F. Finster, J. Smoller, S.T. Yau, Particle-like solutions of the Einstein–Dirac–Maxwell equations. Phys. Lett. A 259, 431–436 (1999) [3]S. Iwasawa, N. Sawado, Multishell Dirac fermions in the Einstein-Dirac system. Phys. Rev. D 112, 064046 (2025)