The answer is to get a more powerful solid state amplifier. Unless the guitarist wants to hear tube distortion from an overdriven tube amp. The caveat when it comes to amps has been stated and restated --- the comparison of amps occurs when an amplifier is driven well within its specified limitations of power. Anyone who complains about amplifier distortion as a reason for preferring a tube amp really should reframe his mindset. That's like complaining complaining about your Honda's Civic's performance as you drive to drive it on the racetrack. The answer is to get an amplifier that can handle what you throw at it.
All arguments go out the door if someone is intentionally trying to achieve the sound of tube amplifier distortion.