Conversational information seeking (CIS) systems aim to model the user's information need within the conversational context and retrieve the relevant information. One major approach to modeling the conversational context aims to rewrite the user utterance in the conversation to represent the information need independently. Recent work has shown the benefit of expanding the rewritten utterance with relevant terms. In this work, we hypothesize that breaking down the information of an utterance into multi-aspect rewritten queries can lead to more effective retrieval performance. This is more evident in more complex utterances that require gathering evidence from various information sources, where a single query rewrite or query representation cannot capture the complexity of the utterance. To test this hypothesis, we conduct extensive experiments on five widely used CIS datasets where we leverage LLMs to generate multi-aspect queries to represent the information need for each utterance in multiple query rewrites. We show that, for most of the utterances, the same retrieval model would perform better with more than one rewritten query by 85% in terms of nDCG@3. We further propose a multi-aspect query generation and retrieval framework, called MQ4CS. Our extensive experiments show that MQ4CS outperforms the state-of-the-art query rewriting methods. We make our code and our new dataset of generated multi-aspect queries publicly available.