In fact, there really are no ways to increase the number of spells you can cast.
I think the best way to increase the number of spells you can cast are enchanted items. At face value, 1 point of refresh can give you a 7 uses item (1 use from the initial slot, 3*2 uses from the 3 remaining slots from the refinement). If you spend a point of specialization on casting frequency, each enchanted item slot gives you an additional use of an item, which will quickly give you a lot of spells to work with. If you put the spells you use most often into items, you will last quite long. Keep your stress open for spells you need to adjust on the fly, and you should be good for anything that's going to happen.
On the other hand, Harry casts not that many spells in any given scene, I believe. Not without a sponsor, anyway.
For sponsored magic, there are a few things you can do, without actually attaching yourself to a sponsor and its whims:
Temporary location of power:A location of power for sponsored magic only costs 3 points of refresh, but as a wizard with full evocation and thaumaturgy, it only costs you 1 point of refresh. If your GM is up for it, you could tap into a location of power (for example a ley line or a storm) for one scene by spending a fate point per the temporary upgrade rules. That way, you could get quite a bit of mileage out of that one fate point. Of course, any sponsor debt taken here should have an effect later, but for the moment, the wizard should be able to dish out quite a bit.
Self sponsored Magic:Some of the powers on the custom power list that I actually like. Self sponsored magic is a form of extremely powerful specializations. The Merlin would have self sponsored magic (wards), for example, which allows him to raise wards at evocation speed and with some debt taken to himself to increase the power.
Of course you should discuss with your GM/group how debt to yourself plays out, since that is a bit weird. In the case of the Merlin, I imagine, the magic would sort of backlash into his behavior, forcing him to use the turtle tactic on most problems, wall yourself in and sit it out, since that's sort of the mindset of wards. Even if attacking the problem would clearly be the better way to go.