What do you do about nonstop email spam from overseas?

I personally (and my company more broadly) receive nonstop email spam from offshore recruiting agencies about 'a candidate that they have on C2C' (this apparently means something in the shady H1-B contracting world). They have no legally-mandated unsubscribe button or address listed. I have personally asked 1 company to unsubscribe me I believe 15 times now (we're up to 4-8 for the other firms). They're hosted by Tata Telecommunications, and I've started forwarding the spam to abuse@tatatel.co.in, but I highly doubt Indian regulators are going to jump in here.

Yes, Outlook has their emails go to spam now, but that's just another folder in my inbox. I am specifically interested in having their domain flagged so as to put them out of business at least temporarily. I've been forwarding their emails to Spamcop as well, but I'm not really clear what that does.

Is there a body other than Tata Telecommunications that I can appeal to? If they were hosted by a US company I'd complain to them. How do you report a spamming operation so as to knock them out?