In the grand scheme of things, my pullups have been one exercise where I don't see much progression. I've "always" been able to do 3-5 pullups by nature, and even now, after several years, I still wouldn't call it progress. Granted, the 5-7 reps I do now are more quality reps, but I'd definitely expect more progress.
I am beginning to resign myself to the possibility that it's simply my routine that isn't allowing me the best progress in that area.
My usual routine...
...consists of a 3-day split. Push, pull, legs. You know what I mean. On pull-days, pullups are my first exercise, and I've been doing every set/rep scheme known to man. Everything from 8x3 to 3x8, varying grips, and adding weights on belt on the first few sets.
My attempted change-up lately...
...has been to throw in some pullups at the end of the workout on push day and leg day too, just to increase the frequency at which I do pullups. And I do feel like that's been helpful. Whenever I get back to pull day, I can often do 1-2 more reps total, but that might also be because it's a good day in general.
What would you recommend I do in order to progress here? As mentioned, my goal is to progress into muscle-ups. My reps now are pretty good, and I can pull myself up pretty explosively, to the point where I get my chest to the bar. And I mainly do pronated grip pullups, although after I've done that, I tend to change it up for variation. Everything from supinated (chins) to neutral grip.