Recently, the source separation performance was greatly improved by time-domain audio source separation based on dual-path recurrent neural network (DPRNN). DPRNN is a simple but effective model for a long sequential data. While DPRNN is quite efficient in modeling a sequential data of the length of an utterance, i.e., about 5 to 10 second data, it is harder to apply it to longer sequences such as whole conversations consisting of multiple utterances. It is simply because, in such a case, the number of time steps consumed by its internal module called inter-chunk RNN becomes extremely large. To mitigate this problem, this paper proposes a multi-path RNN (MPRNN), a generalized version of DPRNN, that models the input data in a hierarchical manner. In the MPRNN framework, the input data is represented at several (>3) time-resolutions, each of which is modeled by a specific RNN sub-module. For example, the RNN sub-module that deals with the finest resolution may model temporal relationship only within a phoneme, while the RNN sub-module handling the most coarse resolution may capture only the relationship between utterances such as speaker information. We perform experiments using simulated dialogue-like mixtures and show that MPRNN has greater model capacity, and it outperforms the current state-of-the-art DPRNN framework especially in online processing scenarios.