You can attach a seat to your SUP board, provided the board has d-rings on which the seat can be hung. You should also take into account that you need a kayak paddle (with a blade on both sides) to be able to paddle like this.
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Aquatone says about the Kayak SUP Seat
Turn your SUP board into a sit-on-top kayak instantly with this Kayak Seat. The soft padded seat with solid back support construction provides comfort for all day paddling and relaxing on the water.