Raising floor in mudroom 4 inches and putting in tile?

We have a mudroom off of our kitchen, on our main floor (above a full-height basement). I’ve stripped the old vinyl flooring off the floor in the mudroom, and would like to raise the floor 4 inches – to meet the hardwood floor in the kitchen – and probably tile. Is there a convenient way to do this without removing the floor completely and raising it from the basement? i.e. can I build some kind of floor structure on top and put down ply? It’s a small area, and currently it is chipboard (under the vinyl) laid down over the rafters. Thanks in advance, all!

With 4", you have a few choices. Keep in mind that if there's a door into this area (likely from outside into the mudroom), 4" means redoing the door and maybe the steps leading up to it, if there. There are rules about keeping step heights within certain limits and you'll likely need to rebuild the door rough opening which means tearing out some wall.

If you're willing to do all of that, you could build a grid of 2x3's attached to the floor, then a layer of say 5/8" ply followed by a membrane like Ditra and then tile. Adjust the height of the 2x material to get the height you want. While 5/8" is the absolute minimum ply thickness you'd want to tile onto, if you make your spacing on the 2x material at say 12" or even a bit smaller, it would be plenty stiff enough.

The other way would be to make a mudbed out of what is referred to as deckmud. This is a dry mix of 4-5 parts sand to 1 part of portland cement by volume. WHen I say dry, that means only add enough water to the mix so that when you grab a handful and squeeze, it holds together but doesn't drip. WOrking with this is like packing wet beach sand. You'd want a layer of plastic or tar paper on the floor with lath on it, then pack the stuff level at exactly the height you need. This can get the floor perfectly level at exactly the height you want.

Or, if you're willing to tear out the existing subflooring, you could sister some joists onto the existing ones, but raised to the height you need after installing (I'd use 3/4" T&G here) new subflooring, then your choice of tile prep material, cbu, membrane, etc., then tile. You'd want the sistered joists to be deep enough to have at least half of it overlapped with the existing ones and use some construction adhesive and screws and nails to hold it all together.

There are innumerable ways you can raise the floor as long as it is a "step down" room which would not require modifying the doors. Just build a substructure on top of the existing joists, (not rafters), adjusting the thickness to allow for the subfloor and tile thickness.