Catalyzes the interconversion of (R)- and (S)-stereoisomers of alpha-methyl-branched-chain fatty acyl-CoA esters (PubMed:8020470, PubMed:9106621). Acts only on coenzyme A thioesters, not on free fatty acids, and accepts as substrates a wide range of alpha-methylacyl-CoAs, including pristanoyl-CoA, trihydroxycoprostanoyl-CoA (an intermediate in bile acid synthesis), and arylpropionic acids like the anti-inflammatory drug ibuprofen (2-(4-isobutylphenyl)propionic acid) but neither 3-methyl-branched nor linear-chain acyl-CoAs (PubMed:8020470, PubMed:9106621). a (2S)-2-methylacyl-CoA = a (2R)-2-methylacyl-CoA (25R)-3alpha,7alpha,12alpha-trihydroxy-5beta-cholestan-26-oyl-CoA = (25S)-3alpha,7alpha,12alpha-trihydroxy-5beta-cholestan-26-oyl-CoA (2R,6)-dimethylheptanoyl-CoA = (2S,6)-dimethylheptanoyl-CoA Optimum pH is 6-7. Lipid metabolism; bile acid biosynthesis. Lipid metabolism; fatty acid metabolism. Monomer. Belongs to the CoA-transferase III family.