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I am a junior/mid lit lateral and I have had 3 interviews (screener, 2 callbacks) at a BL firm I really liked. I also got the vibe that they really liked me. A small piece of that vibe (but certainly far from all of it) is the fact that every partner/associate I did my most recent round with responsed to my thank-you email very warmly, more than half of whom encouraged me to reach out if I have additional questions. I realize that seems insignificant, but I only think I’ve ever gotten a response to my thank you email once and it was for a job I ended up getting.

I’m about a week out and no word from the firm yet.

My question is whether, in this scenario, it’s ever a good idea to take them up and ask them a question by email...and, if so, what types of questions would be good to ask?

I’m probably not going to do this (most I would do is email recruiting to ask about timing, I think), but I was just curious about people’s thought on this.

I don't see any harm in asking the recruiter if they have a sense of timing. Particularly with July 4 breaking up next week, if the hiring committee isn't meeting this week, it may be a few weeks before you hear back. No reason not to check in so you aren't stressing for two weeks unnecessarily.