I agree, a four-truck shay would be interesting. They didn't do very well on the true logging railroads, but when the WM(?) heard about the low speed HIGH horsepower ratings that they had, they put it to work as a yard switcher. It's a wonder more railroads didn't catch on. Then again, I'm unaware of how successful it was as a switcher.
They weren't used primarily as yard switchers, but the Chesapeake & Ohio Railway (C&O) purchased 16 four-truck shays from Lima, designated as Class C-9, that were used on various branch lines with steeper-than-average grades from the early 1900s through the late 1920s. They did their share of switching at various coal mines on the branches and being shorter in length that a Mallet, they conserved space on the short switchbacks found on some branch lines.
In a
level yard, Shays weren't all that more powerful than conventional rod steam locomotives. For example, the three-truck, 150 ton, Shay, built in 1921 for the Greenbrier, Cheat & Elk RR (engine #12 on the GC&E) had a tractive effort just slightly less than a USRA heavy Mikado, which meant that both locomotives had practically the same train starting capacity on
level track. However, that 150-ton Shay was capable of exerting 28 percent greater pull on a 4-percent grade and more than double the pull on an 8-percent grade vs. the Mikado. The Shay's forte was its ability to handle more cars on steep grades.
The GC&E and Shay collaborated to add a fourth truck to #12 in 1933, and in the process, created the heaviest Shay (at
196 - 203 tons) ever operated. See pic of the four-truck #12
here.