Customized text-to-video generation aims to produce high-quality videos that incorporate user-specified subject identities or motion patterns. However, existing methods mainly focus on personalizing a single concept, either subject identity or motion pattern, limiting their effectiveness for multiple subjects with the desired motion patterns. To tackle this challenge, we propose a unified framework VideoMage for video customization over both multiple subjects and their interactive motions. VideoMage employs subject and motion LoRAs to capture personalized content from user-provided images and videos, along with an appearance-agnostic motion learning approach to disentangle motion patterns from visual appearance. Furthermore, we develop a spatial-temporal composition scheme to guide interactions among subjects within the desired motion patterns. Extensive experiments demonstrate that VideoMage outperforms existing methods, generating coherent, user-controlled videos with consistent subject identities and interactions.