That sounds like you have one cable for power in and another power cable going out to another portion of the circuit. If so your plan kills part of the circuit.
He may have a European Washer Dryer Apt. Style stackable. Years ago they wired receptacles split with two circuits top for Dryer, bottom for Washer. Not even sure you can still get those units.That sounds like you have one cable for power in and another power cable going out to another portion of the circuit. If so your plan kills part of the circuit.