Vanilla image completion approaches exhibit sensitivity to large missing regions, attributed to the limited availability of reference information for plausible generation. To mitigate this, existing methods incorporate the extra cue as guidance for image completion. Despite improvements, these approaches are often restricted to employing a single modality (e.g., segmentation or sketch maps), which lacks scalability in leveraging multi-modality for more plausible completion.In this paper, we propose a novel, simple yet effective method for Multi-modal Guided Image Completion, dubbed MaGIC, which not only supports a wide range of single modality as the guidance (e.g., text, canny edge, sketch, segmentation, depth, and pose), but also adapts to arbitrarily customized combinations of these modalities (i.e., arbitrary multi-modality) for image completion.For building MaGIC, we first introduce a modality-specific conditional U-Net (MCU-Net) that injects single-modal signal into a U-Net denoiser for single-modal guided image completion. Then, we devise a consistent modality blending (CMB) method to leverage modality signals encoded in multiple learned MCU-Nets through gradient guidance in latent space. Our CMB is training-free, thereby avoiding the cumbersome joint re-training of different modalities, which is the secret of MaGIC to achieve exceptional flexibility in accommodating new modalities for completion.Experiments show the superiority of MaGIC over state-of-the-art methods and its generalization to various completion tasks.