Can H-4 visa (no EAD) holders take an unpaid internship?

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I am an LLM student on H4 (no EAD). My college offers paid and unpaid supervised externships (optional classes) for 2/3 credits as part of our course. Can I participate and work in an unpaid supervised externship on H4 without EAD?

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Sure. I don't see any problem for you, the employer should watch out for themselves.