[en] A new relativistic n-body scattering formalism is introduced, which explicitly satisfies the cluster property, and reproduces the analytic structure of the lowest-order Feynamn graphs. Applied to a three-particle system, this formalism defines an alternative form of the relativistic Faddeev equation; specific formulas are presented for the case of an s-wave separable interaction. A generalization of this equation is proposed for the purpose of three-particle data analysis, and is shown to provide an exactly unitary description in a form suitable for chi²-minimalization techniques. This exact description further suggests an approximate formalism, which effectively generalizes the isobar model (including realistic thresholds and some three-body cut structure). When applied to a four-body system in lowest order, the formalism defines a model for diffractive production of three-body states such as 3π, Kππ, Nππ, etc. Combined with subsequent rescattering of the three-particle system, this treatment confirms the recent result of Aitchison and Bowler concerning very strong production-resonance interference; this is shown to be related to the difference in the off-shell structure of the corresponding amplitudes. In the particular context of diffractive three-body production, this translates to significant differences in calculated cross sections when the subenergy dependence of the isobar amplitudes is neglected. It is further shown that off-shell (vertex) corrections to the Deck amplitude can produce both strong subenergy dependence and dramatic changes in the cross sections (as a function of three-body mass). These effects are illustrated vai an analysis of the 1⁺0⁺ state of Kππ produced in the reaction K+p → K⁺π⁺π^-p at 13 GeV/c. A Q₂ state of Kπ is found at 1.2 GeV (compared to 1.4 GeV in previous analyses), whereas a Q₁ state (coupling predominantly to rhoK) is found at 1.3 GeV. Implications for A₁ production are discussed