In classification tasks, such as face recognition and emotion recognition, multimodal information is used for accurate classification. Once a multimodal classification model is trained with a set of modalities, it estimates the class label by using the entire modality set. A trained classifier is typically not formulated to perform classification for various subsets of modalities. Thus, the model would be useful and portable if it could be used for any subset of modalities. We refer to this problem as the multimodal portability problem. Moreover, in the multimodal model, classification accuracy is reduced when one or more modalities are missing. We term this problem the missing modality problem. This article proposes a novel deep learning model, termed KModNet, and a novel learning strategy, termed progressive learning, to simultaneously address missing modality and multimodal portability problems. KModNet, formulated with the transformer, contains multiple branches corresponding to differentk-combinations of the modality setS. KModNet is trained using a multi-step progressive learning framework, where thek-th step uses ak-modalmodel to train different branches up to thek-th combination branch. To address the missing modality problem, the training multimodal data is randomly ablated. The proposed learning framework is formulated and validated using two multimodal classification problems: audio-video-thermal person classification and audio-video emotion classification. The two classification problems are validated using theSpeaking Faces,RAVDESS, andSAVEEdatasets. The results demonstrate that the progressive learning framework enhances the robustness of multimodal classification, even under the conditions of missing modalities, while being portable to different modality subsets.