My home has a step down living room. It has carpet on it, but i want to make the floor level with the rest of the house it is about 2.5 inches step down. People keep tripping. I then either want to put new carpeting in or tile floor.
Install a new plywood subfloor elevated on sleepers to match the existing adjacent floor surfaces.
A sleeper is a piece of dimensional lumber (such as a framing stud) ripped to the desired thickness.
Especially if you are considering tile, gypcrete (floor leveler - lightweight self-levelling gypsum concrete) might be the best solution. If there's even a remote chance you might ever want in-floor radiant heating, place the PEX tubing for that before pouring the gypcrete (and depending on the floor there now, possibly place an inch of insulation and 1-1/2 inches of gypcrete) - you don't need to hook that up right away, but it's cheap and easy to do with the pour, expensive and tedious to try and do later.