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Let’s say I applied for an internship at 10 law firms for the same month and get a positive response from 3 of them. I am pretty sure some people have been in this spot. What do you do? I mean you can’t just ghost the HR. But if I mail them that I have secured an internship elsewhere, does that not shut all doors for any potential internship/recruitment with them?

Please help a homie out if you’ve dealt with such a situation.
Short answer: Just be polite about it and request them to re-schedule it. Some T2s/boutiques etc go for it, but most T1s don't. As for burning of bridges, that's a risk that con only be minimised, not extinguished.

I lost out on a known T2 internship that way when I got a T1 instead, and the HR ended up blocking my mail address.

However, that's been the only unpleasant experience I've had that way. In my second year, for example, I was able to convince a boutique for a deferred internship in the subsequent semester break.

As a general note, I guess it's best to focus on 2-3 firms and make best possible applications for them. If you want to have backup options, it's best to go for lesser known names/firms you're not very keen on. Such a plan may reduce such risks.
Ask if any of the internships can be postponed to a future date. Otherwise just say something urgent came up, so you can't attend the internship