Amino acid ligation to cognate transfer RNAs (tRNAs) is catalyzed by aminoacyl-tRNA synthetases (aaRSs)-essential interpreters of the genetic code during translation. Mammalian cells harbor 20 cytoplasmic aaRSs, out of which 9 (in 8 proteins), with 3 non-aaRS proteins, AIMPs 1 to 3, form the ∼1.25-MDa multi-tRNA synthetase complex (MSC). The function of MSC remains uncertain, as does its mechanism of assembly. Constituents of multiprotein complexes encounter obstacles during assembly, including inappropriate interactions, topological constraints, premature degradation of unassembled subunits, and suboptimal stoichiometry. To facilitate orderly and efficient complex formation, some complexes are assembled cotranslationally by a mechanism in which a fully formed, mature protein binds a nascent partner as it emerges from the translating ribosome. Here, we show out of the 121 possible interaction events between the 11 MSC constituents, 15 are cotranslational. AIMPs are involved in the majority of these cotranslational interactions, suggesting they are not only critical for MSC structure but also for assembly. Unexpectedly, several cotranslational events involve more than the usual dyad of interacting proteins. We show two modes of cotranslational interaction, namely a "multisite" mechanism in which two or more mature proteins bind the same nascent peptide at distinct sites and a second "piggy-back" mechanism in which a mature protein carries a second fully formed protein and binds to a single site on an emerging peptide. Multimodal mechanisms of cotranslational interaction offer a diversity of pathways for ordered, piecewise assembly of small subcomplexes into larger heteromultimeric complexes such as the mammalian MSC.