When I tried to create something simillar to inbox floating action button i thought about creating own custom component.
It would be simple frame layout with fixed height (to contain expanded menu) containing FAB button and 3 more placed under the FAB. when you click on FAB you just simply animate other buttons to translate up from under the FAB.
There are some libraries which do that (for example https://github.com/futuresimple/android-floating-action-button), but it's always more fun if you create it by yourself :)