Multi-task audio source separation aims to separate the audios collected from the complex environment into three fixed types of signal sources. Existing methods like EAD-Conformer usually take a manually designed model to process the separation. These networks may be sub-optimal since it is hard for humans to train and test all possible architectures. Especially, it is natural to adopt different optimal sub-structures for decoding different types of signals, which, however, is very hard for humans to enumerate. In this paper, we quantitatively analyze the redundancy of the EAD-Conformer network and customize an effective and efficient search space. We propose an efficient K-path search method to search for the optimal architectures from the Conformer-based search space. We conduct a comprehensive search in terms of block numbers, head numbers, and channel numbers. Extensive experiments demonstrate that our searched architectures outperform existing methods in terms of efficiency and effectiveness.