In this paper, we present PCoTTA, an innovative, pioneering framework for Continual Test-Time Adaptation (CoTTA) in multi-task point cloud understanding, enhancing the model's transferability towards the continually changing target domain. We introduce a multi-task setting for PCoTTA, which is practical and realistic, handling multiple tasks within one unified model during the continual adaptation. Our PCoTTA involves three key components: automatic prototype mixture (APM), Gaussian Splatted feature shifting (GSFS), and contrastive prototype repulsion (CPR). Firstly, APM is designed to automatically mix the source prototypes with the learnable prototypes with a similarity balancing factor, avoiding catastrophic forgetting. Then, GSFS dynamically shifts the testing sample toward the source domain, mitigating error accumulation in an online manner. In addition, CPR is proposed to pull the nearest learnable prototype close to the testing feature and push it away from other prototypes, making each prototype distinguishable during the adaptation. Experimental comparisons lead to a new benchmark, demonstrating PCoTTA's superiority in boosting the model's transferability towards the continually changing target domain. We will make our code publicly available.