Supers can be used with tbh's if you're willing and able to lift supers. But don't forget that the beauty of a tbh is embodied in the fact that capped combs can be removed as they are filled without having to deal with supers.
This hive has a super which was made the same size as Langstroth supers, but there is no rabet for the bars to fit into. A Langstroth super could be used, especially well when turned upside down so that the rabet is to the bottom. The top bars come all of the way out to the ends of the super, and the bars are at right angles to the tbh bars which doesn't seem to cause any problem.
It's good to use a bait comb in the super to pull the bees up to work the foundation strips on the top bars of the super. Occasionally bees will start to build some comb on the top of the tbh bars before working on the super bars.
The cover is tied onto this hive and super by using a nylon cord.
This 5-bar nuc has a 5-bar super on it that is the same depth as the hive body. Three of these supers can be put on top of a 20-bar tbh. If one were to be used at the rear of a tbh with entrances on one end, then the brood combs which should be toward the front could be checked if desired without disturbing the super.
If a notch is cut into a top bar, bees can pass up through the notch. The queen could also, but I haven't had this occur yet.
A bar can be removed at the rear or at the front, and this gives bees good access to the super. The comb in the tbh next to the gap may be drawn out so as to interfere with a comb being replaced. This is no problem if it is in an area which contains comb to he harvested.
If it is desirable to have a lot of access from the brood area to the super, as perhaps in raising queens, a queen excluder bar works well.
This is the top view of a 5-bar nuc with a queen excluder bar, which I devised, in place. The bar was made by taking sections from a wire excluder and attaching it to blocks and strips to give a composite bar the same width, 35mm, as a top bar.
If the bar is removed and turned upside down, a bar that is affixed a bee space below the wire excluder can be seen. Some additional notches were added to that bar to increase access to the bee space below the excluder wires.
A foundation strip is waxed into this section, then when the excluder bar is in place, the foundation can be drawn out to preserve comb spacing and provide more area for brood or storage. The foundation strip shown in this photo is at least twice as wide as necessary. A strip about half an inch wide gives better and more rapid attachment of the comb to the top bar.
Since there are no frames around the combs in the supers, isn't it possible that the bees will attach the bottoms of the combs to the top bars of the hive on which the super is placed?? Yes, this can occur, especially if shallow supers are used.
How can the super be removed without tearing the combs badly? One simple solution is to take a strong cord, piece of fine music wire, or monofilament fishing line and pull it along between the bottom of the super and the top bars of the tbh. This will cut any attached comb free.
The super can then be tilted up on end and a comb at the side freed of any attachment at either end. That comb can be removed, brushed free of bees, and the comb cut off into a havest container. After the first comb is removed, it's easy to get to the next.
Alternately, a bee escape board could be used with the super and after an appropriate period of time, the entire super could be brought to the processing location for honey.