While the Model 1873 was a very popular rifle, its pistol caliber cartridge did leave a segment of the market unaddressed. Winchester wanted a rifle that could chamber the larger and more powerful cartridges popular with long range hunters, and the Model 1876 would be that rifle.
Early attempts to enlarge the 1873 action to use the .45-70 Government cartridge were unsuccessful, for two reasons. First, the cartridge in its 45-70-500 infantry configuration was simply too powerful for the toggle lock design that had been the core of all Winchester’s rifles back to the 1860 Henry. In addition, the elevator mechanism used to feed the rifle had to be sized to a specific (and fairly precise) overall cartridge length. The variety of different bullet weights used in the .45-70 did not affect use in single shot weapons, but did cause problems for Winchester’s repeater.
The solution was for Winchester to design a new round for it’s scaled-up Model 1876. This was the .45-75, and it used a relatively light bullet and a bottlenecked case similar to the general design of the .44 WCF from the Model 1873. This bottleneck improved obturation, preventing powder fouling from leaking around the cartridge case and into the working parts of the rifle. This was not strictly necessary though, as new chambering of the 1876 would be quickly added, including the .45-60; a straight-wall shortened version of the .45-70 Government round.
While it did not blow the doors off the factory like the 1873 had, the Model 1876 was a popular rifle with its intended audience, with tens of thousands of rifles sold to men including Theodore Roosevelt.