Methods and systems are provided for operating a branched exhaust assembly in a vehicle engine in order to increase catalyst efficiency and reduce engine emissions. In one example, a method may include, during a cold-start condition, flowing exhaust first through a three-way catalyst then through an underbody converter, then through a heat exchanger and then through a turbine, each exhaust component housed on different branches on the branched exhaust assembly. After catalyst activation, exhaust may flow first through the turbine, then through the underbody converter and then through the three-way catalyst, and during high engine load, exhaust entering the turbine may be cooled in order to reduce thermal load on the turbine.