Parallel won't do anything to the sound, series will do a little bit, but it seems kind of silly to go to 18v just to burn through twice as many batteries. If you're happy with the fresh 9v sound, you could put 2 in parallel and use lithium batteries for the longest possible battery life.
I think 18V would just add more attack, since the higher voltage is just going to make the peaks more abrupt.
What sort of set-up are you using for your amp and pedals? You may be able to get what you're looking for just by getting new tubes or something. Especially if you have EL34 tubes, you could try a 6L6 or 6V6 for more clean headroom.
There's also this http://www.precisionmusictech.com/xbat.htm You'd have to contact them about the availability of the 18v version though, I haven't seen any. GuitarElectronics just has the 9V, and if you ran that with a battery also in your guitar it would be 18V, but it might blow the circuits in the X-Bat(I tried putting 18V in it and it fried the fault protection, giving me a nasty popping sound when the battery got put on the hot signal output when plugging in and unplugging, it still worked fine other than that though).