We report here the Zn(II)-catalyzed convergence of two metastable and isostructural polyesters to an isomeric polymer having a hyperbranched architecture. Ring-opening transesterification polymerization (ROTEP) of 4-carbomethoxyvalerolactone (CMVL) under Brønsted catalysis is known to give the linear polyester PCMVL. We show here that this can be isomerized to the equilibrated (and highly branched) polyester EQ-PCMVL. Analysis of the fragments obtained from eliminative degradation of EQ-PCMVL were critical in the formulation of its structure. The isomerization of PCMVL to EQ-PCMVL is a direct consequence of the presence of the second ester functional group in the CMVL ester-lactone, a rarely studied class of monomer. Zn(II)-catalysis of the ROTEP of the isomeric β-lactone, 2-(2-carbomethoxyethyl)propiolactone (isoCMVL), as well as isomerization of the isostructural linear homopolymer derived from that isomeric monomer, led to the same EQ-PCMVL. These results suggest a new strategy for the introduction of branching into various polyesters.