That sounds like a technical question that you'd have to ask officials at your school to answer. In my experience, each school has its own rule for how they decide whether or not to confer more than one degree for overlapping coursework.
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But I have a broader question to ask you: This question is not to discourage people working on associate's degrees, but if you're on this forum I'd have to ask... what does it matter whether you can get both from the same school?
If you're on this forum I'm assuming you want to get into medical school. Each medical school publishes its admissions criteria. None that I've ever seen says anything about an associate's degree.
In the world of academics at the med school level, an associate's degree is about as relevant as a junior high school diploma.
What does matter is having a bachelor's degree + specific coursework.
