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If it's the former, then perhaps the problem lies more with the adjacent grade than the patio. Regrading can be accomplished at much lower cost, and without the help of professionals or special equipment.
If it's the latter, then you might be looking at a replacement rather than a fix, depending on how much you're figuring on raising it. I can't think of anything that you can pour on top of an exterior slab in a thin layer that will raise the elevation, level the area to accomplish drainage, and at the same time have a satisfactory longevity before it starts to crack and spall.