Involved in the glyoxylate assimilation cycle used to regenerate acetyl-CoA and produce pyruvate as universal precursor for biosynthesis. This reaction involves an intramolecular CoA transferase that catalyzes the reversible transfer of the CoA moiety from the C1-carboxyl group of mesaconyl-CoA to the C4-carboxyl group. It does not require free mesaconate as CoA acceptor. 2-methylfumaryl-CoA = 3-methylfumaryl-CoA Partially inhibited by hydroxylamine. kcat is 840 sec(-1) for isomerase activity with 2-methylfumaryl-CoA. Optimum pH is between 7.5 and 7.8. Optimum temperature is 55 degrees Celsius. Homodimer. Under autotrophic growth conditions. Belongs to the CoA-transferase III family. Mesaconyl-CoA isomerase subfamily.