I'll tell you what I do on my OHP day.
5/3/1 OHP, 5x5 (week1), 10x3 (week2), 12x2 (week3) Push Press using the last work-set weight of the OHP.
No one really told me to do this. I just started doing it because I had hit somewhat of a wall with my OHP. I thought it would be nice to add Push Presses because it would get me used to holding some heavy weight overhead.
Got a lot of inspiration from FSL. I did some calculating, and I found out that 95% of my OHP was around 75% of my PP. So it kind of worked out pretty nice.
I initially tried doing 5x5 push press all the way through. It was just too hard (for me).
If you can handle that load, I'm sure that'll work really well too!
I personally don't like the idea of making the PP the main lift, simply because I believe if your goal is to increase absolute strength, moving something from a dead stop w/o any help is most effective.
That being said, I love the PP as a movement itself, and believe it helps a lot with coordination and learning to actually control the strength you develop.
BTW, if someone thinks this is a bad idea, please let me know! I'm not sure I will change what I'm doing, but I'm constantly seeking constructive criticism.