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I really like 2 particular firms, screener interviewed with them about 10 days ago, would really like to work at either of their offices. They are smaller "regional" firms in a secondary market. Would it be awkward to email them to re-assert my interest? Should I?

I'd probably send to recruiting but no it's not weird

I don't think it helps. Some people think differently. This topic has been argued a thousand times on TLS and it's usually a 50/50 split of opinion since no one has real data.