It would help if the circuit is capable of handling the increased voltage.
All caps should be rated at twice or better than the voltage applied.
For the Caesar...
The TL022 can handle 15v, but not 18v — check the datasheet to be sure.
RC4558 says max is 18v.
The bottle-neck is the delay chippage:
The 3207 max voltage is 10v!
The 3102 max volts is 12v.
So, while you could theoretically run the pedal at a higher voltage, so long as you feed the delay chips what they need, I'm not sure you'll net much headroom out of running a higher voltage.
If my engine's redline is 6500 RPM, then I like to go up to 6000 max, and even then around town driving I'm probably barely getting to 4,500 RPM on average — better gas mileage and less wear&tear.
So while a TL022 can handle 15v, I'd go with 12v; for the 4558 I'd go with 15v etc.
For THIS circuit, I'd just build it stock and run it stock, as that already puts me right at the limits of my capabilities.
That's not to say that more headroom can't be had, just that I don't know how and need to defer to the circuit-power experts.
So... BUMP! Calling all circuit gurus, clean up on aisle 1...