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Would it be serious faux pas to ask my 2L SA firm whether I can also act as a remote research assistant for a professor part-time? Does anyone else have experience doing this?

I do it--but I wouldn't ask the firm. My professor just understands that I do work when I have the time--otherwise, there's no pressure. If the RA job is going to be more demanding (e.g., mandatory 15-20 hours per week) then I would probably forego the RA position. In terms of helpfulness, the SA position is likely a better resume line--that is, of course, unless the professor has really good ties to your dream firm or something. Regardless, just prioritize. Also, take into account compensation--my RA position pays between $12-15/hr. whereas my summer gig is NYC market--big difference.