It actually came about because I was really squeezed for time - I wanted to do extra sets (4 or 5) on the press and squat, and still wanted to keep the pull ups in the frame.
So I figured out a conservative number of pull ups that I could just walk up to a bar and do perfectly, regardless of fatigue, any time, anywhere: about 50% of my max worked well. So starting off with 2 reps if my total was 5; if your total is 3, perhaps start with 1. The point was for it to be so achievable I didn't need 2mins' rest beforehand (heresy, I know

I then just did that number of reps immediately after each set of my main lifts. Finished the squat/press set, walked straight over to the bar, did 2 pull ups, then I set the timer for 2mins in order to rest properly for my next set of squat or press.
It was easy to accumulate up to 10 sets of pull ups this way each session. I never went anywhere near failure. It didn't affect my other lifts because it was such a low number each time and, anyway, I always rested at least 2min before lifting.
The following week I would then nudge maybe half of the sets up by 1rep, or whatever felt realistic. Over the course of a block I went from something like 10x2 reps to 10x5-6 reps per session; the volume really adds up over the week. At the end of the first block I actually managed a single set of 10 pull ups, which I didn't expect.
So yeah, might not work for everyone but it did for me!