To build volume with pullups, complete your sets with negative pullups as gp describes (nb: at least three seconds down from chin over bar to full hang) when you fail the full pull-up (at least two seconds up, from full hang to chin over bar) any more.[1]

>> I am trying to build upper body strength

1. Keep a diary recording every session. 2. Stay away from the bench press. Focus on your back chain, arms, and grip: deadlifts, pullups (weighted, when you can do a set of 20 body weight), and overhead presses. Add squats and weighted press-ups if you insist. (Make sure you get taught both proper form and proper warm-up sequencing and always use them!)

Observe that these are all exercises that most people hate doing. For good reasons: they are hard work, and nearly all the gain is in your back, which you can't see in the mirror.

1. I used to see a lot of people doing what they claimed were pullups, with only a ten inch range of motion. Not helpful in real life. Start from a full hang: shoulders under hands, arms straight.