In the bowl of a standing mixer, beat the egg whites with the sugar just until combined. Set the bowl over a saucepan of simmering water and whisk constantly until the mixture is very warm. Return the bowl to the mixer and beat the egg whites at high speed until stiff and glossy, about 5 minutes. Add the butter, 2 or 3 tablespoons at a time, beating at medium-high speed, until glossy and smooth. Add the Grand Marnier and beat until incorporated.