Chess/Checkers Board

This is a Chess/Checkers board I am currently working on. The board is made with 1.5" X 1.5" pieces of Brazilian Cherry and Birds Eye Maple. The board is then framed in Red Oak. I have one coat of Tung Oil on the board so far and I like the way it looks. I have never used it before and plan on applying a second coat. I was wondering if I can still use a polyurethane over the oil to make it more durable, or just more coats of the oil? Any help would be appreciated.