If I'm remembering this correctly from physics class then in math terms this is described as U=C*n*R*T where U is the energy, the constant C varies depending on

If I'm remembering this correctly from physics class then in math terms this is described as U=C*n*R*T where U is the energy, the constant C varies depending on the degrees of freedom the molecules of the gas have, n is the molar amount of the gas, R is the ideal gas constant, and T is the temperature. From that perspective it seems impossible to raise the pressure without also raising n resulting in a higher U even if you maintained a constant T while you did so?