Olympic weightlifter Bill March strict pressing over 300 lbs.
Since bench pressing became too painful due to a partially-torn labrum, the overhead press has become my main upper body lift. Hitting bodyweight has still eluded me, however; my best strict press is 190 at 205. I'm currently weighing in around 193-195, and my press is somewhere back in the neighborhood of 185-190, so I'm reasonably close to a bodyweight press. There seems to be no magic formula for strict pressing, other than a decent amount of volume and a commitment to form. My current program, which I believe will net me a 200 lbs press very soon, is below.
Sunday: Overhead Press--115*5, 135*5, 145*5, 155*3-5, 165*1-3, heavy single (175, 180)
Dumbbell rows for 3 sets, high reps.
Thursday: Overhead Press--115*5, 135*5, 145*5, 155*5, 160*5
Some sort of arm work, usually for high reps.
All of these presses are done out of the rack, yet I think it's beneficial to switch it up with clean and presses on occasion. I've found you can't press quite as much after cleaning, but the increased difficulty of the start position helps when you return to pressing out of the rack. Making sure your lats are tight and your arms are tense definitely aids your pressing when attempting heavy weights. As far as recommending assistance exercises, the push-press isn't bad to add on occasion at the end of a workout. I'll add five pounds to whatever my last set was, and bust out a couple sets of 3. With the push press, you want to make sure your legs are just aiding the initial movement of the barbell; otherwise, it becomes more of an accessory lift for the jerk than the strict press. Back when I benched, I thought the two lifts were intertwined, for when one increased, the other would as well. I've found that dips and triceps extensions resulted in elbow pain, though my elbows suck. Thus ends my pressing recommendations.