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Being a light machinegun, you can of course swap your barrels to let your current one cool down while you use a spare. This involves taking the entire barrel and its breech assembly out of the gun to put in the new one, which incidentally makes it very easy to convert these guns between 7.92mm Mauser and .30-06 Springfield on the fly. Earlier versions were a bit finicky with the changes, but it was simplified in later iterations.
Pictured here is a 1907 produced gun, chambered in 7mm Mauser for a Brazilian contract (7mm Mauser being 7.92mm Mauser necked down for a smaller projectile, you can of course swap as easily between this cartridge and the two previously mentioned ones just as easily). If you went through the trouble, you could probably have a barrel made for .270 Winchester, and it should work fine if made properly.
These guns have a long history, seeing their first real combat use in the Russo-Japanese war, while Russia didn't perform the hottest at the time overall, their good use of the Madsen machineguns made a very strong impression, observers from different countries made note of the use of this new kind of weapon which people weren't yet quite sure of how to best use. It would go on to see use in the First World War, the Russian Revolution and Civil War, the Mexican Revolution (on all sides), the war and strife in China's "Warlord Era", the Spanish Civil war, along with various other conflicts of the "Interwar Period" between the world wars, continuing to see use in World War 2 itself (including the Winter War and Continuation War), and even afterwards.
Much of the later use was in second line units as more cost effective and efficient designs came in use, though dated, they did work perfectly fine, and they were still bought new and used for rear echelon troops by Nazi Germany as late as 1942, as it was a usable gun which Madsen was capable of producing while Denmark was occupied.