Can you increase your max reps by increasing your max strength?
If you max out at 10 or fewer bodyweight pullups, all you need is pure strength training. In the immortal words of Steve Baccari, “Don’t worry about strength endurance; you don’t have enough strength to endure.”
If your repetition maximum is between 10 and 20 reps, you would benefit from repping out—but it is not necessary. Increasing your 1RM strength through low rep heavy training will allow you to build up to 20 strict bodyweight only pullups without ever practicing them.
If your repetition maximum is higher than 20 reps, you need to develop crazy strength on the bottom of the pullup.
One Russian authority recommends partial repetitions, 5-10cm or 2-4” starting from a dead hang, eventually building up to an additional weight equal to one’s bodyweight.
The logic is straightforward: a reserve of starting strength will allow you to take off fast and finish your rep using inertia. That means that the weaker muscles that help you to clear the bar with your chin, such as the biceps, will do little work and this work will be brief.
In addition, each rep will be over quicker, which translates into a lesser challenge to the grip. Anyone who has exceeded 20 strict pullups will tell you that as the reps climb, forearm pump often becomes a big problem. (A topic for another time: hanging on a bar or farmer’s walks will not fix it.)
For your heavy pullup starts we recommend a parallel grip narrower than your shoulders as the safest.
Get tight, get hollow, and pull.
Do not explode; save that for your bodyweight only high reps.
Keep your elbows in. Stop before the top of your head reaches the level of the bars, and lower under control.
On the bottom let your shoulders shrug but do not relax them.
Start with a weight less than your 1RM for a full range tactical pullup and build up from there. Keep your reps per set in the 5-15 range; a shorter range of motion allows higher reps while keeping it a strength exercise. 3-5 sets once a week will do, in addition to your regular pullup training.