Why doesn't she want you to take another little? Is it personal, in that she doesn't want you to be spoiling anyone other than her? Or is it uncommon for someone about to graduate to take a little, and because of her position as New Member Ed that she doesn't want you to do it?
With only a few months left, there won't be much time to develop the relationship, and if she is an underclassman she will be orphaned prematurely. If these are her objections, I would let it go. .
Or, I'd wait until after the new members rank sisters, and if a particular girl ranks you and you really want her, you might be able to make a case then. But, just because you aren't someone's Big doesn't mean you can't spoil her and have a close friendship.
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