Why can’t I extrude from the base bone twice?
You can only extrude from the Tip of a bone. What you want to do is snap your 3D cursor to the root of that bone and deselect all bones in edit mode. Then hit Spacebar and Add a new Bone. Select that bone (yellow) and in F9 (top right little box with ‘IK’ on the end of it) make it the child of the bone whose root you wanted to extrude from.