Importing multiple Blender files in Unity

This might be more of a question for a Blender targeted forum, but I am not really sure whether the solution I am looking for is Unity related or not. Basically, I have a model that I have animated in Blender with a simple walking animation. If I export this to Unity, everything is fine. How would I save that animation in Unity, create a new animation(say, a run or kick animation, etc), and then when I load the exported .FBX model to Unity have both animations available to work with? As far as I can tell, there is not an option in Blender to save the current animation, and then start over on a new one.

Thanks for any help!