I had some of the best results of my life about a decade ago with the Korte program, doing all three lifts three times per week with lots of volume and relatively low percentages.
The weekly setup I use now is:
- SSB Squat/Deadlift/Buffalo Bar Bench
The intensities fluctuate throughout the week with this. As you can see, pretty limited exercise menu, just some targeted variations in addition to the powerlifts and some lat work.
This represents an increase in volume and frequency from what I have used in the past, so I do not have competitive results to cite yet, but I can tell you my work capacity and technique have improved a lot, and after a couple weeks of feeling horrible basically all the time, my body seems to have begun to accept this workload.
With respect to what Russian lifters do, I think there is nearly as much variety in training styles and methodologies in Russian powerlifting as there is in American, but their approaches are grounded in the lessons of weightlifting, while ours have until more recently been grounded in bodybuilding, which leads to some of the differences you probably have in mind. Lately, though, our better lifters, at least in the raw/tested camp, have tended to gravitate towards more frequency and specificity. It's always possible for the pendulum to swing back, but with the results at IPF raw worlds and at the national meet improving so dramatically year-to-year, it looks like the value of just doing the lifts more and more is being borne out.