I wouldn't run any of the 'standard' pedals like the Boss with anything by 9v, but I do need to check with Broughton and Keeley as I seem to remember they can even suggest running with 18v for more headroom.
I’ve got the Keeley Bassist and a Broughton HPF. I run both at 9V without issue and both are squeaky clean sounding devices. YMMV.
Official published spec for the Bassist on the Keeley website is 9V. I don’t think it’s generally wise to deviate from the standard supply voltage unless you have a very real reason to do so. So unless you actually need additional headroom there’s not much point in pursuing it.
The Broughton HPF can be run with anything from 9V to 24V. But if you’re not dealing with a line level signal, you shouldn’t need any additional headroom and running with a standard 9V should sound just as good. I seem to recall in the Broughton superthread Josh said something to that effect as well.