To put it simple, yes, you can. Reducing Vcc will reduce gain. But this will make the transistors work in a less linear region, thus increasing intermodulation and cross modulation.
Here's a hint: place a 9V regulator at the input, feed the circuit with a variable voltage from 12 to 20 or 24V. The amplifier won't be affected, but you can use the variable voltage to drive some electronic attenuator. This is my idea: connect an LDR to the loop, have a LED illuminates the LDR, the LED will have cathode to GND, anode to a 10V zener in series with an appropriate resistor. Send 12V and you'll have max gain. Increase voltage and the LED will become brighter, the LDR's R will get lower, thus attenuating the signal with no distortion.