If you verify that it's brushless (3 larger wires and a set of 5 small ones for the halls going to the motor), then all you need is higher voltage for more speed unless you're looking for much more powerful acceleration. That means more batteries and a new controller. Yes, if it's brushless the motor will handle 96V without issue. According to the Ebikes.ca simulator the X409 (using a 408 sim and adjusting for the additional turn in the windings), it will get you to a 30mph cruising speed on about 83V from the battery, so you'll need 26-27s of Lifepo4 or 23-24s of Lipo or LiMN. You'll only be running 800W or less so the motor shouldn't be strained at all, though if it's a lot of stop and go, you may want to direct some extra air flow at the motor. Check how warm it getting under your hardest existing operating conditions to give you a baseline, and then also feel it for heat a number of times early on after the change.
If the motor is inside the velo with you, then it's going to be hard to beat the quiet little X409. A lot of the newer motors are noisier, which would be amplified inside a velo. If you wanted more like 40mph or better and far more zippy acceleration, then I'd have a different suggestion for you, but just for that kind of moderate speed, what you have is fine. If you've put a whole lot of miles on it, then I'd say crack it open and change the bearings, and coat the stator with some rust prevention, but there's always a risk of messing something up by opening a motor that is working fine. I'm of the mindset "If it ain't broke, don't fix it".
If you do open it up, put alignment marks on each cover with a corresponding mark on the magnet backing ring. I use a center punch to put 1 dimple on each on one side and 2 on each on the other. That way everything can go back together exactly as before.