While you're there, rent a power washer. A thorough blasting of the tile and grout would probably help water flow to the drain better. Just being mindful not to blast any one spot too hard lest the power of the water cause actual damage.
And while you have the grates off the drains check to make sure they're clean, and that the pipe from the is also.
An atrium drain will only help when the water rises above the level of gunk that blocks the lowest parts of the cover. It's bad to have standing water, for any number of reasons. But the one I'd worry about most would be the water then finding leaks down to the area below.
So don't just assume a change to the grate is the only part of the solution.
Hey Bill I greatly appreciate the advice. My situation is a little different from the OP. We have a bilevel house and the lower level has a walkout to a 8X8 concrete patio, and then the ground slopes up about 4 feet to the yard. In the middle of that concrete patio is a 4.5 inch diameter circular drain that goes to the drain tile and to the sump.
I've had some plumbers look at it, and they all scratched their heads lol. One suggested a trench drain, but that's very expensive to install.
You're right about making sure it's not clogged...should I think about having it snaked?
An atrium drain would be better than the current situation. If the water rises up more than about 2 inches it starts leaning against the sliding glass door and risks leaking into our family room.
Right now we keep a long-handled broom/brush there and we push the crud off it when it's filling up, and it drains quite quickly when we do.
We keep it very clean but we have mature trees and we live in the country and pollen/dust/leaves/seeds etc always find their way to the area, and then the water leads them to the drain as it flows.