By lyophilization from 40% acetic acid solutions, bovine pancreatic ribonuclease A forms several three-dimensional (3D) domain-swapped oligomers: dimers, trimers, tetramers, pentamers, hexamers, and traces of high-order oligomers, purifiable by cation-exchange chromatography. Each oligomeric species consists of at least two conformers displaying different basicity density, and/or exposure of positive charges. The structures of the two dimers and one trimer have been solved. Plausible models have been proposed for a second RNase A trimer and four tetramers, but not all the models are certainly assignable to the tetramers purified. Further studies have also been made on the pentameric and hexameric species, again without reaching structurally clear-cut results. This work is focused on the detailed modeling of the tetrameric RNase A species, using four different approaches to possibly clarify unknown structural aspects. The results obtained do not confirm the validity of one tetrameric model previously proposed, but allow the proposal of a novel tetrameric structure displaying new interfaces that are absent in the other known conformers. New details concerning other tetrameric structures are also described. RNase A multimers larger than tetramers, i.e., pentamers, hexamers, octamers, nonamers, up to dodecamers, are also modeled, with the proposal of novel domain-swapped structures, and the confirmation of what had previously been inferred. Finally, the propensity of RNase A to possibly form high-order supramolecular multimers is analyzed starting from the large number of domain-swapped RNase A conformers modeled.