Allright, its a kind of a workaround but here is how it works:

1. If your Animation inside the FBX is a Humanoid (Avatar/Mecanim..) Animation you have to convert it into a Legacy animation first. Click on the file, import settings, pick animation, convert to legacy.

2. Place a Animation-Compontent and increase the size to 2. Insert your Legacy animation in, and insert a new empty animation in.

3. In the Unity-Animator copy all read-only keyframes and paste them into your new empty animation.

4. Profit. The empty Animation is changeable

Allright, its a kind of a workaround but here is how it works:

1. If your Animation inside the FBX is a Humanoid (Avatar/Mecanim..) Animation you have to convert it into a Legacy animation first. Click on the file, import settings, pick animation, convert to legacy.

2. Place a Animation-Compontent to you Animateable Gameobject and increase the Animation Size to 2. Insert your Legacy animation in, and insert a new empty animation in.

3. In the Unity-Animator copy all read-only keyframes and paste them into your new empty animation. You have to use: "ctrl+c / ctrl+v"

4. Profit. The empty Animation is changeable