Many proteins form paralogous multimers - molecular complexes in which evolutionarily related proteins are arranged into specific quaternary structures. Little is known about the mechanisms by which they acquired their stoichiometry (the number of total subunits in the complex) and heterospecificity (the preference of subunits for their paralogs rather than other copies of the same protein). Here we use ancestral protein reconstruction and biochemical experiments to study historical increases in stoichiometry and specificity during the evolution of vertebrate hemoglobin (Hb), a α2β2 heterotetramer that evolved from a homodimeric ancestor after a gene duplication. We show that the mechanisms for this evolutionary transition was simple. One hydrophobic substitution in subunit β after the gene duplication was sufficient to cause the ancestral dimer to homotetramerize with high affinity across a new interface. During this same interval, a single-residue deletion in subunit α at the older interface conferred specificity for the heterotetrameric form and the trans-orientation of subunits within it. These sudden transitions in stoichiometry and specificity were possible because the interfaces in Hb are isologous - involving the same surface patch on interacting subunits, rotated 180° relative to each other - but the symmetry is slightly imperfect. This architecture amplifies the impacts of individual mutations on stoichiometry and specificity, especially in higher-order complexes, and allows single substitutions to differentially affect heteromeric vs homomeric interactions. Many multimers are isologous, and symmetry in proteins is always imperfect; our findings therefore suggest that elaborate and specific molecular complexes may often evolve via simple genetic and physical mechanisms.