As far as I see it, you can use as many aspects as you want to boost a thaumaturgy effect, even at the speed of evocation. The problem with a thaumaturgy effect of too much complexity is, that you also have to gather up the power in 1 roll, so you would probably need even more aspects to invoke here. Or, as you already have sponsored magic, push the entire backlash onto your sponsor and have fun trying to get out of your debt ever again.
Also, you don't have any time to prepare the thaumaturgy spell, as you would have with any usual thaumaturgy ritual, so anything you are using would have to be made up on the fly, and there is only so much you can do. Then again, your sponsor might jump in there.