I once gave my birds 30% protein feed. I didn't notice a difference, but maybe that's because they were only on the food for a week, and they have a large free range area.
You likely wouldn't. Law of diminishing returns.
In terms of the things most people might measure - frequency of lay, size of egg - the difference between a 16% CP and a 20% CP feed of identical AA profile is only a couple of percent - which for a prime layer means a handful more eggs a year (likely more than 2, less than 10) and about a 1g increase in average egg weight. Things you will never notice w/o careful measuring and good notes. There are some other things (faster, less stressful molt, improved disease resistance, often improved behaviors) which are harder to quantify.
The difference between a 20% CP feed and a 24% CP feed of identical AA profile is usually estimated at a little less than half the improvement above. Going to 30%? les sthan half again. On the other hand, the amount of nitrates (ammonia, primarily) goes up dramatically - the body expelling protein it can't use that day.
At least, that's the case for adult commercial layers.
Effects are more noticed with birds just hatched and growing. Faster growth, larger eventual size, improved feed efficiency, greater disease resistance. But even then, you can reach a point where more protein isn't a net benefit.
and like all dietary changes, it takes a bit before those changes start to express themselves - the older, more "complete" the bird, the longer it takes.