It's great that you want to pay her dues and are in a position to do so. But it's not like she can shop around and "buy" a middle of the road (cost-wise) sorority. Recruitment doesn't work like that.
If you have a budget in mind, tell her what it is, and make anything above and beyond that her responsibility- she will be an adult. It is a bonus that you are helping her financially. She can easily get a job to help pay for extras such as t-shirts, photos, date parties, etc.
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