Recently, the rise of large-scale vision-language pretrained models like CLIP, coupled with the technology of Parameter-Efficient FineTuning (PEFT), has captured substantial attraction in video action recognition. Nevertheless, prevailing approaches tend to prioritize strong supervised performance at the expense of compromising the models' generalization capabilities during transfer. In this paper, we introduce a novel Multimodal, Multi-task CLIP adapting framework named \name to address these challenges, preserving both high supervised performance and robust transferability. Firstly, to enhance the individual modality architectures, we introduce multimodal adapters to both the visual and text branches. Specifically, we design a novel visual TED-Adapter, that performs global Temporal Enhancement and local temporal Difference modeling to improve the temporal representation capabilities of the visual encoder. Moreover, we adopt text encoder adapters to strengthen the learning of semantic label information. Secondly, we design a multi-task decoder with a rich set of supervisory signals to adeptly satisfy the need for strong supervised performance and generalization within a multimodal framework. Experimental results validate the efficacy of our approach, demonstrating exceptional performance in supervised learning while maintaining strong generalization in zero-shot scenarios.