A super simple method I love for developing reps in particular exercises is to hit it every day.
Yes, you read that right.
1 set every day
The trick is to wave the load through the week.
On day 1, test. Push to technical failure and record that number.
Every subsequent day do a number anywhere from 50% to 95% of that number.
Retest every 7 days.
A week of push ups could go:
Monday: 35 (max)
Then retest on the following Monday
This works with most sub maximal exercises.
Try it with Goblet Squats, Kettlebell Snatch, Push Ups, Bodyweight Squats (although the numbers go up fast with these), pull ups (assuming that can already do at least 5)
You can do up to 3 exercises, but make sure that you only do a hard session on one of them on any given day.
For best results, stick to a single movement for a month then put that on the back burner for a while