Entrusting our speech to multiple different corporate actors is always risky. Yet given how most of the internet is currently structured, our online expression largely depends on a set of private companies ranging from our direct Internet service providers and platforms, to upstream ISPs (sometimes...
If such a process existed, the entity in question would almost certainly end up being shut down by that process, unless they find a funny technical loophole around it, in which case that would be a failure of the law that should not be rejoiced by anyone.
But as it stands, that law and process does not exist; ISPs already can and will shut you down for things like downloading copyrighted content (with or without complaints from the copyright holder), tethering without approval, being a technical nuisance in the form of mass port scanning, hosting insecure services and other such stuff. “Hosting a platform solely dedicated to harassment and stalking and ignoring abuse complaints about it” absolutely deserves to be on that list.
Not sure about the US, but in the EU that process does exist: anyone can submit a claim against any domain, and if the “competent authority” which can be a judge or a law enforcement agency, so decides, they add it to a list of domains to be blocked at the ISP level… currently meaning at the ISP’s DNS resolver (use non-ISP DNS resolvers at your own risk), but technically they could request routing or deep packet inspection blocks through the same process.
As far as I know (but this might be outdated), ISPs in the EU are not allowed to play other shenanigans with user’s data.