Point cloud (PC) processing tasks—such as completion, up-sampling, denoising, and colorization—are crucial in applications like autonomous driving and 3D reconstruction. Despite substantial advancements, prior approaches often address each of these tasks independently, with separate models focused on individual issues. However, this isolated approach fails to account for the fact that defects like incompleteness, low resolution, noise, and lack of color frequently coexist, with each defect influencing and correlating with the others. Simply applying these models sequentially can lead to error accumulation from each model, along with increased computational costs. To address these challenges, we introduce SuperPC, the first unified diffusion model capable of concurrently handling all four tasks. Our approach employs a three-level-conditioned diffusion framework, enhanced by a novel spatial-mix-fusion strategy, to leverage the correlations among these four defects for simultaneous, efficient processing. We show that SuperPC outperforms the state-of-the-art specialized models as well as their combination on all four individual tasks. Project website: https://sairlab.org/superpc/.