Extend Automatic Factories to automatically use Parameter Overrides
The current system of Automatic factories in Unity defers resolution when a class's constructor has a dependency of Func<IMyService>. This could be extended to automatically use parameter overrides when it sees a dependency of Func<SomeType,IMyService> and the concrete class implementing IMyService needs a parameter of type SomeType. This would only kick in if an InjectionFactory of the required type wasn't registered.
Mykola Musiienko commented
While Sebastian's code gets the job done, I believe it doesn't completely match the suggestion -- for example, it requires declaring a factory delegate and registering it in the container.
So, if anyone is still interested in this suggestion, I implemented a Unity extension, which, I believe, matches the suggestion exactly and also is more in line with the Unity's parameterless automatic factories experience.
Sebastian Weber commented
That feature already exists though it is not shipped as part of Unity