3 real beds in one room is not possible in most resorts - definitely not moderates or value. Options include a family suite in All Star Music - one queen size bed, full-size sofa bed, twin-size sleeper chair in the living area, 2 bathrooms. But, that is close to the price of 2 regular rooms in the values. Art of Animation is similar, but way more than the cost of 2 value rooms.
Moderates, I don't think there is anything with a 3rd bed, some rooms have a child-size murphy bed. You cannot book those directly, they give them out to families of 5 first, then randomly.
You may need to look at villas at Old Key West, Saratoga Springs. But, again the 3rd sleeping surface is a sofabed. Unless, you bump up to a 2-bedroom and that is usually more than the price of 2 rooms at moderate.
I find that if you put in 5 in the search for a room instead of 4, you will come up with rooms with a 3rd sleeping surface.