Provided herein are combination therapies involving co-expression of an E2 subunit of a branched-chain alpha-keto acid dehydrogenase (BCKDH) from a skeletal muscle-targeted rAAV.hDBT vector and a liver-targeted rAAV.hDBT vector. Also provided herein are combination therapies wherein an E1a and/or an E1b subunit of the BCKDH complex is expressed from muscle and/or liver following rAAV-mediated delivery targeted to these tissues. Further provided is a pharmaceutical composition comprising a rAAV as described herein in a formulation buffer, and a method of treating a human subject diagnosed with MSUD.