The normal escalation process looks like:
- Users get a bunch of flags on their posts
- Moderators discuss if needed and delete flagged comments as appropriate
- User gets sent a warning message by moderators (privately, so no one else sees that except SE staff, moderators, and the user)
- depending on severity of comments, if you go around actively swearing at people and blatantly violating the Be Nice rule you might not get a warning
- normally this involves some discussion with other moderators
- If this continues, the user may be suspended temporarily
- almost always involves discussion with other moderators
There are a variety of ways this gets tracked or aggregated, I'm a bit hesitant to give too much information here. There's some context in this other meta post I made though specifically regarding comment flags.
Keep in mind that the entire "Be Nice" process is subjective. There's not an automatic way to evaluate "when is too much?" and that at varying times we get accused of being too strict, too lenient, and too biased (on every extreme apparently).
Everyone will have a slightly different "scale" for what level of moderation they want to see. Some would prefer we suspend people for the first minor infraction, some prefer to be way less strict, and everywhere in between.
I can assure you this is an active topic of conversation among moderators too.