That leads to some intriguing questions.

If the game is in private beta, how did you get a copy of it, how did you develop your mod? If you were somehow involved with a private beta you really ought to tread with caution and discus it with the developers before doing any more with it.

You mention targeting multiple games, I'm not aware of any mods that do that sort of thing, as each game executable is unique. I can imagine games with expansion packs that are designed for modding, where you can write a mod for the base game that modifies functionality across both core and EPs.

Games that support modding usually have the explicit blessing of the publisher as part of the modding API and documentation. They often have forums and chat sites to discuss and share the mods. These are also generally the easiest to develop for, and many games have active and supportive mod development communities.

Games that don't support modding directly but get modified generally do not do so with the permission of the company. Exactly how that is handled is up to the company and the nature of the mod. Just because they allow it for one title doesn't mean they allow it for everything: sometimes a major publisher will allow mods on one product but vigorously defend another.