If you add enough that it smothers the grass, you've added too much. Otherwise, it continues to break down, so there's no cumulative effect when you add it year after year. In some ways, that's one of the disadvantages to OM. Since it breaks down over time, you need to add more every year.

Since you asked specifically about compost in a lawns forum, the MOST compost you need on turf is 1 cubic yard per 1,000 square feet. This is a light dusting, easily visible on concrete but completely invisible on a lawn, IF you get it swept in properly. Back when I used compost, I used a push broom to sweep the compost off of the grass blades and get it down to the soil.

I don't use compost as a turf amendment anymore. I don't see the need for it. I create compost behind my garage from "other people's leaves" simply so I don't have to buy mulch for my plants.

Rather than using compost on the lawn, I simply fertilize with organic fertilizer. Organic fertilizer is a real, fresh food for the microbes. By the time rotting organic material decomposes into a fresh smelling compost, most of the food value of the compost is gone and you are left with a lot of beneficial microbes. Certainly applying a lot of beneficial microbes is not a bad thing, but you really should not need to do that annually even if you live in the desert. As long as you do not let the microbes die from lack of moisture, they should serve you indefinitely. If you feel the need to apply new microbes, consider using compost tea.

Organic fertilizer is a lot less expensive than compost. In my neighborhood, a cubic yard of compost costs $35 plus $35 delivery while 1,000 cubic feet's worth of ordinary corn meal costs $1.50 to $3.00 depending on how much you use. The cost per 1,000 square feet of compost tea is more like $0.35 but again, it has only microbes, no food value for those microbes.

The amount of organic fertilizer it would take to smother your lawn is about 80 pounds per 1,000 square feet. Besides killing your lawn, an application that heavy is also accompanied in a few days by a sour stench, much like spoiled milk, that will last seemingly forever until the material is more fully decomposed. The amount of compost that most certainly will smother your lawn is 4 cubic yards per 1,000 square feet. There is a formerly beautiful St Augustine lawn in my neighborhood that applied compost that heavily early last April. Five months later, even with 40 inches of rain, they still have a dead lawn. Normally St Augustine will creep 10 feet in all directions per growing season, but when you smother it, you're luck to get much creep at all.