Making increase is easy with all mediums. I met a Bulgarian beekeeper earlier this month who was going over to this system as he was buillding up his colonies in order to turn semi-pro.
Once the coloney is into two bodies slip a queen excluder between them and after a few days you can quickly see where the queen is by the presence of eggs. Then take away the other box and introduce a new queen to it after a short delay.
Of course you can do this with full depth brood boxes but Langstroth Mediums, being a bit smaller, fill up more quickly. A Langstroth box of 10 Mediums gives almost exactly the same usuable brood area as a standard BS National box. I use the term "useable" as the Langstroth has fewer frames but in a poly hive the queen will use all of them whereas in a BS National wooden hive the queen will normally often ignore the outer frames.
The two Medium brood boxes, which is the standard way of running these colonies gives exactly the same brood area as a Jumbo Langstroth with the advantage of lower weight of the individual boxes and possibly improved horizontal movement of bees in the brood area due to the gap running through the middle between the upper and lower frames. This may reduce swarming due to improved transfer of queen substance but I am not aware of any research confirming this.
The Bulgarian called colonies on all mediums as the "Farrar" system. I can't find any reference to this other than a C L Farrar wrote about beekeeping many years ago. I would be interested for a specific reference if anyone knows it.