I would recommend using a marble threshold in the doorway between the two floors. You could install it flush with the old tile while being 1/4" higher than the new tile. Marble thresholds come in different varietes such as natural white, cultured (beige or white), and travertine and are beveled on the edges, making a nice transition from one surface to another.
Michael Prachniak - Expert Tile and Stone Consultant and Writer, Owner - Tile Productions
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