As Mooz already said in the comments, there are no mentions of houses with more than one ruler.
But often the Lord gives some of his responsibilities to other people.
The most common example found in the books would be the Castellan. His responsibility is the defense of a castle, fort or city.
Also there are examples where there is a Lord but he is not the actual ruler.
The most familiar example would be Robert Arryn who is the Lord of the Vale but, because he is under-aged, Littlefinger was granted the title Lord Protector and is currently the de facto ruler.
The Game of Thrones RPG from Telltale features House Forrester, a minor house from the north sworn to House Glover of Deepwood Motte.
The game introduced the title of Lord Sentinel which is granted by the Lord.
The Lord Sentinel has total power over the House and is only second the actual Lord. So the position of the Lord Sentinel is quite similar to the position of the Hand of the King.