We construct a general parametrization of the baryon octet and decuplet mass operators including the three-body terms using the unit operator and the symmetry-breaking factors M^d=diag (0,1,0) and M^s=diag (0,0,1) in conjunction with the spin operators. Our parametrization has the minimal number of operators needed to describe all the octet and decuplet masses. Investigating the likely size of the three-body terms, we find that contributions of the three-body hypercharge splittings are

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... e to those from the one- and two-body isospin splittings and that contributions of the three-body isospin splitting operators are very small. We prove that, in dynamical calculations, one must go to three loops to get the three-body terms. We also find that the suggested hierarchy of sizes for terms in the most general expression for baryon masses that involve multiple factors of M^d and/or M^s does not hold strictly for dynamical calculations in heavy baryon chiral perturbation theory: terms of a given order in a meson loop expansion may appear both with the expected factors of M^d and M^s, and with one factor more.