Here's a very effective way of increasing the number of full handstand push-ups (HSPU) you can do, even if you're stuck. It's a tactic I used before entering a strength cycle again, and it worked very well after a little adaptation. Here's the initial plan:
1. Practice HSPUs on Mondays, Wednesdays and Fridays.
2. Progressively increase the total volume of work until I increase the difficulty of the sets.
So here's what I did:
1. I tested the maximum number of perfect HSPUs I could do (15).
2. Chose to do sets of 10 reps, because I estimated I could use this number with 5 sets.
3. Decided I would start out with 5 sets of 10 reps (5x10), and do one more set every training, until I could do 10 sets of 10 reps (10x10). And all my sets should be done in an hour or less.
4. Once I could do 10 sets of 10 reps, I'd switch to sets of 11 reps, and start over again with 5 sets.
5. Keep going until I could do 10 sets of 15 reps.
By doing that, it would've taken me 2 weeks to add one repetition to my sets, and 10 weeks to go from 5x10 to 10x15. That would be an increase of 100 reps per training, or 200% of the initial work load. But I didn't take into consideration that after a 10 sets training, 5 sets would still be a bit too much, and with one more repetition per set, it would be too fast a progression. So I decided to start again with the same principle, but starting with 2 sets instead of 5. That way, reaching 10 sets of 15 repetitions would take 15 weeks instead of 10, which in my opinion is too much time spent on a single exercise, so I decided to change my training plan after doing 10 sets of 13 reps. My maximum number of HSPUs has increase nevertheless, and I'm convince such a technique can help someone who's stuck increasing his/her number of reps again.
If you follow that kind of program, I would also recommend you train twice a day, doing something different (something excluding upper body pushing or pulling). Here's what my training sets looked like:
M: 2x10, 5x10, 8x10, 2x11, 5x11, 8x11, 2x12, 5x12, 8x12, 2x13, 5x13, 8x13
W: 3x10, 6x10, 9x10, 3x11,6x11,9x11, 3x12, 6x12, 9x12, 3x13, 6x13, 9x13
F: 4x10, 7x10, 10x10, 3x11, 7x11, 10x11, 4x12, 7x12, 10x12, 4x13, 7x13, 10x13
If you want to adapt this kind of training to your needs, there's four parameters you'll have to play with. The first one will be the frequency of your trainings. You can do more sessions on where you don't follow this program, but make sure you're able to go through. I chose to do it three times a week, and I suggest you do the same. If you do a very high volume, you can do it only twice a week. The second parameter is the number of sets you want to start with (I chose 2), and the third is the number of sets after which you want to increment (I chose 10). The bigger the difference between the two, the longer it will take you to add one repetition, and the higher the numbers you pick, the more volume you'll do. The last parameter is how many reps you should start with. Change these parameters to your convenience, but make sure you stay realistic.
And if you have a hard time progressing, figure out the reasons why you're not progressing anymore. It is good to vary the exercises we use (not necessarily a big variation), and vary the type of training we do.