Alternate History, WWI:
The Pedersen device was designed to turn a 5 shot heavy caliber bolt action rifle into a 30 shot light pistol caliber semiauto. The idea being that once you get into the trench fast and furious fighting is more the norm.
The Pedersen device was a colossal failure, only spared from historical ignominy by the fact the war ended before it was deployed. But the idea is incredibly cool. Beyond that, it's an illustration of the contradiction of the traditional trench war. The armies were organized around full power, long range range rifles, but once you get into trenches, these rifles are nearly unusable and pistols and submachine-guns become more ideal.
So I thought, what if they had developed a less cool gun but to fit the same niche? Imagine a 30 round 32ACP full size pistol. Only slightly larger than a 1911, once a doughboy was over the top they could easily transition to this gun for trench fighting. It has to be about the same weight as a Pedersen device (less than 3lbs). Small and light is necessary so as not to weigh the troop down withh too much stuff. A second 8-10 lb SMG is just not feasable. For caliber, 32 ACP is about the same power as the 30 Pedersen rounds that were developed for the device and the round was developed before WWI. 32ACP is well suited for simple blowback pistols, keeping costs down.
So what would a Trench Pistol look like? We start with the magazine. Looking back with historical knowledge, a double-stack, double-feed magazine is most reliable, but harder to engineer a gun for. However they did exist at the time. As 32ACP guns are already very thin, this increase in width and complexity is a cost the design can bear. However, I don’t think we could build a traditional angled pistol mag, so stick mags like the ones for the Pedersen would be likely, resulting in a straight up and down grip, much like the Sketchin and MAC series of machine pistols. While we have the capacity, no need to make it more difficult to use by having it be a machine pistol, simple semiauto blowback action will suffice. So imagine a scaled up 1903 Colt. 4-5” barrel, a slide and feedramp designed for the double-feed magazine.
If the historical floodgates were open the VZ61 Skorpion (a 32ACP machine pistol) would fit this role perfectly, but it has the advantage of 40+years of Submachine-gun and pistol development. The amount of innovation and things that the Skorpion builds on just wouldn’t be available. Alternately, issuing every soldier a Browning 1903 with several extended 10 round single stack magazines would be immediately possible and nearly as effective.
With more development, but lesseffort then the Pedersen device, a pistol that accepted doublestack magazines would have been feasable, or something similar to the Mauser layout with the extended doublestack / doublefeed magazine in front of the pistolgrip and the manufacturing simplicity of blowback operation.
I think that such a "Trench Pistol" would serve the same purpose of a Pedersen Device. It'd be available sooner as development would be shorter and based on existing guns and designs. It has compromises. 32 ACP is a much lighter cartridge then 45ACP or 9mm Luger or even 380 auto, the three more common pistol and submachine-gun cartridges. But I think the capacity increase and ease of deployment would have been worth it. 9mm and 45ACP SMGs (and pistols) are significantly more costly to manufacture at the time as well as bulky with more recoil.
If the war had carried on even longer, a simple openbolt blowback machinepistol with stock slightly larger then a Broomhandle Mauser could have been developed using the same magazines. This stretches the design ability of the era, as cheap open-bolt guns made with stampings don't appear until the Sten of WWII. At the time everyone thought guns had to be finely milled and machined steel and wood. The idea of using extrusions and quickly milled castings to get more guns onto the field quickly didn't seem to register.