Ryfujk

We recently purchased a new home (yes, new construction); the home is a modern-style three story 1800 sqft detached home with a cantilevered section. There's a carport under the cantilever, and then the second and third floor sit above the first floor + carport. It's slightly similar-ish to this home, but with two support posts instead of one:
https://photos.hgtv.com/photos/viewer/cantilever-/modern-home-with-garage-and-cantilever-carport

Anyway, the floor of the second story has a small slope over the cantilevered portion (3/8" total recession over 10 feet). Apparently this was due to a builder mis-measurement, and is not a foundational problem with the home (the third floor is perfect and has no slope). We put a clause in our purchase agreement that if we find that the floor slopes further, they will fix everything, and we negotiated the price down significantly after the inspection uncovered this, assuming we could live with it.

Furthermore, the beam right where the cantilever begins is obvious and forms almost a small "mountain" in the floor, which would make leveling more complicated since we'd have to level the entire floor to this top point instead of just the cantilevered portion.

I guess you could visualize a cross section of the floor (very roughly!!) this way:

_________________________---___

                               ---------

                         /

                         |

                  cantilever starts here

The floors are all engineered hardwood.

So, finally to my question:

While I am able to live with it, It's definitely been on my mind to go and fix this someday if possible, and I was wondering what options we have and if this is even possibly a DIY project?

I read a few interesting posts mentioning the use of "purlins" like here, here and here.

Could I conceivably use the current engineered hardwood and do a 'leveling' project, or would I almost certainly need to replace the flooring on the whole floor?

Is this a reasonable-ish DIY project, or should I run far away from the idea and just hire people? In that case, would I be looking at prohibitive crazy-costs? Is this all just a wild idea?

If it is useful as a data point, I'm in Seattle, and the floor area is about 33'x20'.

Just looking for perspectives and advice. Thanks all!

You need to get professionals to do this, imho, as the structure will need supporting while the floor-base is sorted out.

That structure has significant weight and supporting it while providing sufficient access to the bits that need repairs / replacement is not a simple task.

Honestly, if they tried to sneak that by you I'd say all is fair in love and war. I would pile all things heavy in the farthest reaches of the cantilever section and force it down. Only if you are able to hire someone else to do the repairs and have them pay for it. That's despicable. The cantilevered section has no foundation so that part can't be a foundational problem. It does tell us that the load it's carrying from the floor above and its own floor is too great. I wouldn't jump to conclusions and suggest it's unsafe or anything like that. They said it was a mis measurement which means they knew about it and chose to not disclose it. It's like selling a painting that you know is a fake. That cantilever section of the house is a defining feature and if anything in the house needs to be right that's it.