Recently, substantial research has been conducted on sequential recommendation, with the objective of forecasting the subsequent item by leveraging a user's historical sequence of interacted items. Prior studies employ both capsule networks and self-attention techniques to effectively capture diverse underlying intents within a user's interaction sequence, thereby achieving the most advanced performance in sequential recommendation. However, users could potentially form novel intents from fresh interactions as the lengths of user interaction sequences grow. Consequently, models need to be continually updated or even extended to adeptly encompass these emerging user intents, referred as incremental multi-intent sequential recommendation. % We refer to this problem as incremental multi-intent sequential recommendation, which has not yet been well investigated in the existing literature. In this paper, we propose an effective Incremental learning framework for user Multi-intent Adaptation in sequential recommendation called IMA, which augments the traditional fine-tuning strategy with the existing-intents retainer, new-intents detector, and projection-based intents trimmer to adaptively expand the model to accommodate user's new intents and prevent it from forgetting user's existing intents. Furthermore, we upgrade the IMA into an Elastic Multi-intent Adaptation (EMA) framework which can elastically remove inactive intents and compress user intent vectors under memory space limit. Extensive experiments on real-world datasets verify the effectiveness of the proposed IMA and EMA on incremental multi-intent sequential recommendation, compared with various baselines.