If it's bodyweight pullups, you can do them a hundred times a day without overtraining. Shit, in the 3 months of Marine Corps boot camp, we did them within 5 minutes of waking up, after each meal, and again before bed. They started us with a pyramid, basically doing 1 pullup, 2, 3, 4, 5, 4, 3, 2, 1...Then adding another set every few days. Sometimes we'd eat twice a day and still never overtrained.
I'll point out again that it's a "bodybuilder's mentality" to worry about overtraining in regards to volume, recovery, or a little lactic acid in the middle of your set.
BUT, if you think you can do WEIGHTED pullups sprinkled 5 days a week into your Bill Starr's power routine, your joints will ache like none other!!