The smallest sensible change, since that is what you asked for and it does not require a programme:
Make the push-up harder so 8-12 is your limit, instead of making it longer. Options, roughly in order:
- Elevate your feet, the higher, the harder. A chair takes most people from 40 to about 12.
- Slow the lowering to three seconds. Same movement, far more time under tension.
- Pause at the bottom for two seconds, which kills the bounce you have probably developed without noticing.
- Move toward one arm: hand on a ball, then archer push-ups.
Pick one, do 3 sets of as many as you can with good form, three days a week rather than daily. Then write down the number every session. When it hits 12 across all three sets, make it harder again.
That last part is the actual mechanism. Everything else is the delivery.