Patio w/ Negative Slope

Our patio has settled into a negative slope toward the house. When it rains, the patio floods like crazy. The patio is 32' x 25', and I'm trying to avoid ripping it up to correct the issue.
There's really nowhere for the water to go left or right. I only have the option of pushing it straight away (rather than toward) the foundation, because it is that way that a drainage easement lies to catch the water by piping it toward it.
Is there a way that I can reslope concrete to re-pitch it, or another way to get rid of the water by some type of drainage method other than installing an outdoor sump pump?
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