Catalyzes the condensation of alpha-ketoglutarate and acetyl-CoA to form (R)-homocitrate. Can also catalyze the condensation of alpha-ketoadipate with acetyl-CoA to form (R)-homo(2)citrate, and the condensation of alpha-ketopimelate with acetyl-CoA to form (R)-homo(3)citrate. These reactions are part of the biosynthesis pathway of coenzyme B and biotin. 2-oxoglutarate + acetyl-CoA + H2O = (2R)-homocitrate + CoA + H(+) 2-oxoadipate + acetyl-CoA + H2O = (R)-dihomocitrate + CoA + H(+) 2-oxoheptanedioate + acetyl-CoA + H2O = (R)-trihomocitrate + CoA + H(+) Organic acid metabolism; 2-oxosuberate biosynthesis. Has been shown to catalyze the formation of trans-homoaconitate (PubMed:9665716). However, probably physiologically functions as an (R)-homocitrate/(R)-dihomocitrate/(R)-trihomocitrate synthase. Belongs to the alpha-IPM synthase/homocitrate synthase family.