Block and IP from creating accounts to online stalk?

Would it be possible to block an IP from social media? I don’t want to go into details for fear of this post being found, but it’s getting pretty creepy. The person I wish to block needs to be able communicate via discord And the like, but I do not want them scouring my social media through alt accounts and leaving anonymous messages and threats. Privatizing my account is not an option as they may have alt accounts I don’t know of, and I can’t sift through THOUSANDS of accounts. Is this possible?