We study the three-body anti-triplet B c → B n M M ′ decays with the SU (3) flavor (SU (3) f ) symmetry, where B c denotes the charmed baryon anti-triplet of (Ξ 0 c , −Ξ + c , Λ + c ), and B n and M (M ′ ) represent baryon and meson octets, respectively. By considering only the S-wave M M ′ -pair contributions without resonance effects, the decays of B c → B n M M ′ can be decomposed into irreducible forms with 11 parameters under SU (3) f , which are fitted by the 14 existing data, resulting in a reasonable value of χ 2 /d.o.f = 2.8 for the fit. Consequently, we find that the triangle sum rule of A0 given by the isospin symmetry holds under SU (3) f , where A stands for the decay amplitude. In addition, we predict that B(Λ + c → nπ +K 0 ) = (0.9 ± 0.8) × 10 −2 , which is 3 − 4 times smaller than the BESIII observation, indicating the existence of the resonant states. For the to-be-observed B c → B n M M ′ decays, we compute the branching fractions with the SU (3) f amplitudes to be compared to the BESIII and LHCb measurements in the future.