I currently have the single Adobe Photography plan but I also want to get Illustrator.
My question is, is there a cheaper way than upgrading to all Apps?
I am a student so can hopefully get student discount if my University is affiliated, but does this mean I will have to cancel my current plan first?
You can get Illustrator on a single app subscription, though I do not think you can get it at the student discount. If you want to see about getting the full plan at the student rate then you should contact Adobe Support and see if they will switch it for you without any penalties.
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Creative Cloud support (all Creative Cloud customer service issues)