Check out in on Houzz https://www.houzz.com/photos/query/sunken-patio

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I don’t know a solution but have a comment: A sunken anything is a recipe for disaster. Remember sunken living rooms? Always a bad idea, IMO.

Another comment: buy the home and live in it a bit before racing forward with a plan that might not be best for the long term. If you’re already considering resale, a sunken patio would likely be a negative selling point.

Would suggest you hire a landscape architect or at least hire a landscape company that has a designer on staff.

We need to see your space so when you take possession post pics ere in comment s I have no idea without context

I don't see any pictures of your existing patio but in my view a sunken patio isn't a good idea, your space would look spacious if all on the same level.

Surrounding the concrete patio doesn't require two levels. The patio can be level with the house entrance. The deck under prep will require amendments to plain dirt for level and drainage. Very doable to make the finished deck, after the surface prep, to be level with the patio. Everything on one level will be the most expansive.

It would be a no from me for a sunken patio. I have seen what happens - ugh.

If you get the right experienced contractor, you can have the wood next to the concrete.

The concrete area will be nice for a grill and maybe a fire pit at the edge, then have the seating on the wood deck.

We need pics to help you though.