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Multiple Sclerosis (MS) is a chronic neuroinflammatory disease and multi-modality MRIs are routinely used to monitor MS lesions. Many automatic MS lesion segmentation models have been developed and have reached human-level performance. However, most established methods assume the MRI modalities used during training are also available during testing, which is not guaranteed in clinical practice. Previously, a training strategy termed Modality Dropout (ModDrop) has been applied to MS lesion segmentation to achieve the state-of-the-art performance with missing modality. In this paper, we present a novel method dubbed ModDrop++ to train a unified network adaptive to an arbitrary number of input MRI sequences. ModDrop++ upgrades the main idea of ModDrop in two key ways. First, we devise a plug-and-play dynamic head and adopt a filter scaling strategy to improve the expressiveness of the network. Second, we design a co-training strategy to leverage the intra-subject relation between full modality and missing modality. Specifically, the intra-subject co-training strategy aims to guide the dynamic head to generate similar feature representations between the full- and missing-modality data from the same subject. We use two public MS datasets to show the superiority of ModDrop++. Source code and trained models are available at https://github.com/han-liu/ModDropPlusPlus.