Answers

When sunken living rooms were the rage, many of them were below grade. Later on some decided that being on all one level was more desirable so it became popular to fill them with concrete to the level of the rest of the home. This was an effective solution for concrete on grade homes.

We recently were asked to lay some beautiful recyeled tiles salvaged from an apartment building lobby in Paris.  But they were too thick by a little over an inch and you would end up with a trip hazzard

We pulled the floor, the sub floor and with engineering, lowered to top edge of the floor joistes, replaced the sub floor, install backer board and then the tile so that it came out perfectly flat. 

Expensive but the end result was beautiful.

Philip Anderson

HDR Remodeling

Berkeley Ca

Assuming that there is a crawl space (not a slab), then the answer would be yes. But there is no way to give any idea as to cost until someone crawled under the house to see how it’s framed, how much clearance (above grade) is existing, if there are any HVAC or other utilities in the way, etc…

Anything is possible. I'm not sure what needs to be done in your specific situation; however, it needs a plan, a budget, and someone to do it.