Which 3D file formats support multiple animations?

I'm working on a 3D application that uses Assimp to import 3D models with animations. Personally, I use Blender to create the models and animations. I'm having trouble exporting multiple animations, however. For example, I'd like to have an idle animation, a walk animation, a run animation, etc. So far I've tried COLLADA and DirectX without much success. The COLLADA export will include the first animation, but not any of the others. The DirectX doesn't include any animation. Which 3D file formats support multiple animations? (Preferably one that Assimp can import. Also, the Assimp website says that it doesn't support .blend files with animation, otherwise I'd just do that.)