I'll also concur that clean output volume is a function of the output tubes, supply voltage, load resistance (to an extent) and output tube bias. Bluesbear is telling you probably the only thing you can try without major surgery to adjust the output stage for more clean volume.
Usually, the actual clean acoustic volume is not the issue in these cases for a non-technical player... usually it's the perception of "headroom" or lack thereof based on the volume knob setting at which the amp starts to distort noticeably.
Fud told you the first big trick: look at removing the 1st stage bypass cap and/or making the cathode resistor larger. I would certainly try to make that cathode resistor a bit larger, as it allows the input stage to handle a hotter signal. But at the input tube the bias is probably large enough to handle it anyway. In that case, you just don't want a ton of amplification.
You might also consider lowering the value of the plate load resistor to reduce output voltage swing.
The signal next hits a volume pot, and you can do some trickery there. I think Rene Martinez tricked SRV a little when he was being difficult about what his amp was sounding like at a specific knob setting by loosening the setscrew on the knob and moving it to indicate a different number at a point that gave the sound SRV wanted. I've seen people that have pet knob settings, who set, say, the Treble on 7 on every amp no matter what the amp's actual voice, then complain the amp doesn't sound right. If they adjusted the knob up or down, they could get "their sound" but they have a mental block that says "a good amp gets my sound when I set this knob to 'X'..."
But just moving the knob is a little cheesy and the customer will surely figure out this was all you did to "fix his amp." But if you want to reduce the signal output from the pot when it is full-up, you can install a resistor between the coupling cap from the previous stage and the input of the pot. That way, full up will never be the full signal strength; there will always be some roll-off. But to really adjust that, you'd ideally be playing through the amp with his guitar, so you will know the knob setting at which the amp starts distorting. This is where a resistor subsitution or decade box really shines. If you know the output level of his pickups, you can fake it somewhat with a signal generator set accordingly.
And you'll want to consider raising the 2nd stage cathode resistor and/or removing the bypass cap for the same reasons you would the first gain stage. Raising the cathode resistor to increase the stage's bias may be even more important on the 2nd stage if it is needing to handle a hotter than normal signal.
There is a balance to be struck with all of these things, and the only sure way of knowing is to adjust them while his normal signal level is being applied to the input. In a perfect world, you'd have 3 to 5 substitution boxes and an alligator clip on the bypass cap legs to dial in each resistor location as he played through the amp until the amp stayed clean on a high enough volume setting for him.