I saw that on your journal just now and responded accordingly, vias vie modifications ot diet or training.
As for what his limit on pull-ups could be after they have increased, it will depend on things like potential power output, muscle size, fat levels, bone density, connective tissue tolerances, rate of Oxygen consumption.
More protein would promote Oxygen potential to the muscles and with ATP creation, by causing vasodilation of bloodvessels, via things like Arginine stimulating Nitric Oxide production.
Things that wouldn't be beneficial for this, would be something like Caffeine, a vasoconstrictor and also other things related to diet like Atheromas and Arterial Plaque, plus Calcification of Arteries, relating to excessive Calcium consumption, which would promote arterial stiffening, as that would also hinder bloodflow.
A more beneficial power to weight ratio would be useful too. More protein could facilitiate this as well, by promoting additional Creatine intake from Fish and certain meats, but also healthy Fats to try and reduce Subcutaneous Fats, to promote a more desirable power to weight ratio, because the individuals natural power reaserves, wouldn't need to be used to counteract as much negative fat weight, allowing for more favourable use of the persons power, by allowing more power to be used, past the point of negative mass counteraction
Example, a 180lb, 6ft person, is more likely to lift more, if he has 15% fat, (as an example figure), and someone else of the same height weighs 2-3 lbs more, simply due to added Fat.
Obviously if the person has more bf% and the same weight, then he definitely would lift less, as he'd have less muscle and thusly less power.
Also pull-ups technique may play a part. If the individual is using a narrow or wide grip, then use the alternate grip to see if that improves or lessens the pull-up potential.