Traditional spatiotemporal models generally rely on task-specific architectures, which limit their generalizability and scalability across diverse tasks due to domain-specific design requirements. In this paper, we introduce UniSTD, a unified Transformer-based framework for spatiotemporal modeling, which is inspired by advances in recent foundation models with the two-stage pretraining-then-adaption paradigm. Specifically, our work demonstrates that task-agnostic pretraining on 2D vision and vision-text datasets can build a generalizable model foundation for spatiotemporal learning, followed by specialized joint training on spatiotemporal datasets to enhance task-specific adaptability. To improve the learning capabilities across domains, our framework employs a rank-adaptive mixture-of-expert adaptation by using fractional interpolation to relax the discrete variables so that can be optimized in the continuous space. Additionally, we introduce a temporal module to incorporate temporal dynamics explicitly. We evaluate our approach on a large-scale dataset covering 10 tasks across 4 disciplines, demonstrating that a unified spatiotemporal model can achieve scalable, cross-task learning and support up to 10 tasks simultaneously within one model while reducing training costs in multi-domain applications. Our code and dataset will be released soon.