The invention relates to the field of couplings, and more specifically to a system for assembling a modular coupling (100) comprising at least a main body (101), a thread (109) around a central axis (X) with restricted freedom to move relative to said main body (101) at least in a direction parallel to said central axis (X), and a distinct toothed part (113) that is fastened to the main body (101) and that presents a set of teeth with at least one front tooth (115) projecting along an axis parallel to said central axis (X). The system comprises a plurality of alternative toothed parts each presenting a different set of teeth for selection as a function of a set of front teeth of another coupling to which the modular coupling (100) is to be coupled.