Methods and systems are provided for coordinated control of a compound boosting system, including a first compressor staged upstream of a second compressor in an engine intake. In one example, a method may include operating the second, downstream compressor in steady-state to achieve an overall pressure ratio across the compound boosting system while operating the first, upstream compressor transiently, based on an airflow shortfall at the downstream compressor. A timing and amount of electric assistance provided to transiently operate the first, upstream compressor may be adjusted dynamically as the pressure ratio across the second compressor changes.