I have a 7X8 concrete slab outside of my back door. It sits in a sort of nook where two sides of it butt up against the concrete basement walls of the house. The problem is that is slopes back towards the house.
I was thinking of breaking the concrete up and pouring over top and having it slope the other way towards the grass. It would only be about 4" deep at the side of the house an a little less than and inch deeper on the side of the yard. I would remove the concrete near the yard, but I would like to avoid removing it all if I can.
Is this advisable?
What would be the best way to proceed?
Thanks in advance for any responses.

You may be able to avoid breaking up the existing slab by cutting slots or grooves into the surface of the existing concrete (thereby providing a porous/scarified base) and "floating" the new material over it to modify the incorrect slope.

If you can't raise the existing slab elevation at the low point(s) by at least 2" (due to your house foundation/weep screed level)... you'll need to cut more depth at that location. Any less than 2" thickness of your overlay will crack/separate.

I personally would not pour over existing concrete the reason being is if the slab is sloped towards the house like you say, something made that happen and usually what it is is water getting underneath your slab making the ground saturate thus making your slab drop and if you put more weight on its going to eventually keep going down. And if you decide to take it out you can replace the elevation with unsaturated gravel , and gravel is cheaper than more concrete down the road, also you might have fixed the moister problem that would have eventually made it down to your basement. Anyhow hope this helps you out and good luck with your project sounds like fun

If the new concrete will be at least 4" thick, you can bore holes through the existing concrete, and put rebar vertically thru it and sticking up about 2 1/2" above the old slab and this will "lock" the 2 slabs together. Also run rebar horizontally tied onto the vertical rebar at about 1 1/2" high, this will reinforce the slab.

Yes put more weight on your already sinking pad, it the most logical thing to do

If the existing concrete is in good shape it can be lifted.
There is a company that pumps material under and it actually raises the whole pad.
I will try and find the website and post it later.

Here is the link
Concrete Lifting

I have seen the company trucks around and was going to try it on a concrete slab but haven't got around to it yet.