Fairy-Max, Sjaak II, and Nebiyu Alien all allow configuration of new variants to some extent, and already out-of-the-box support a large variety of chess variants. They can e.g. be used with the XBoard/WinBoard GUI.
Since you explicitly mentioned Stockfish, I would like to add that I recently started to develop the fork Fairy-Stockfish that is relatively flexible with regard to the addition of new variants. It is still in an early stage of development, so it is not as flexible as the aforementioned alternatives yet, and the addition of new variants can not yet be done via a configuration file (UPDATE 2019/09: user-defined variants via a configuration file are supported now), but via a configuration-like file in the code. The main limitation is that only board sizes equal to or smaller than 12x10 are supported. Its main advantage is that its playing strength is quite high compared to other chess variant engines, since it is based on Stockfish.
The variant you mentioned where the queen can also move as a knight is called amazon chess and is already supported by Fairy-Stockfish. By a 10x10 version of chess, are you referring to something like Grand chess?