Apart from cases where you can do a certain move only once per game, I don't know any variant that imposes larger budgets for certain move types. There are probably good reasons for that; I don't think that rules like that would make very good variants. They lack clarity. The number of obscure and complex rules that can be conceived for strategic games is unlimited; it does not make any sense to support rules that are not, and probably never will be used in practice.
That being said, it already is possible to implement the AsW with a budget of 10 A moves in the Interactive Diagram; you just have to define 11 different piece types for such an 'Elephant', differing in the number of remaining A moves, and make those automatically promote to each other with the aid of the captureMatrix, exempting the W move from such promotion by writing the move as AsW'. It is then up to the game designer whether he wants those types to be represented by the same image, or distinguishable (e.g. by writing the number of remaining moves on them).
Apart from cases where you can do a certain move only once per game, I don't know any variant that imposes larger budgets for certain move types. There are probably good reasons for that; I don't think that rules like that would make very good variants. They lack clarity. The number of obscure and complex rules that can be conceived for strategic games is unlimited; it does not make any sense to support rules that are not, and probably never will be used in practice.
That being said, it already is possible to implement the AsW with a budget of 10 A moves in the Interactive Diagram; you just have to define 11 different piece types for such an 'Elephant', differing in the number of remaining A moves, and make those automatically promote to each other with the aid of the captureMatrix, exempting the W move from such promotion by writing the move as AsW'. It is then up to the game designer whether he wants those types to be represented by the same image, or distinguishable (e.g. by writing the number of remaining moves on them).