The main question to ask yourself is what else do you have to do during your breaks that's a better option? Studying and classes won't get you a job unless you're failing in which case it will lose you a job. If you are doing a bit above average in classes, that's fine.

Jobs you get with contacts, and virtual internships might be only 10% as useful at getting a job as a real physical internship, but that's still 10% more than not doing them at all. Also it is useful to decide if law firm life is for you.

I am currently doing a moot and due to its timeline it stretches over my entire semester, should I take up another internship or should I just focus on my moot and classes?

Let me be frank, the answer depends on where you’re studying. There was absolutely no compulsion or peer pressure to intern beyond the mandatory ones as far as job prospects were concerned at Law School. Just get by, Day Zero will land you something respectable.

You may have to hustle more if you’re from a less prominent college, though.