Private messages are critically important in pushing back this kind of behavior.
It is an appropriate use of private communications to indicate that a user is starting a behavior which the site would rather not see. If there is normally a stigma associated with receiving private communications, you may want to make it clear that this isn't a serious offence, but rather a future warning to cut back on a behavioral pattern.
In this way, you avoid drawing the broader community's attention to the issue, while asking specific users to step back from their potentially caustic behavior.
It is true that caustic behavior spreads in a community - however, it is important to note that caustic behavior generally does not maintain itself, and will die down if the major propagators stop propagating. For instance, if a major user consistently leaves snarky comments, other users will grab onto this as proper community behavior. Ask the major user to stop, and the use of this behavior will generally die down.
If it becomes a serious problem, it may be a good idea to inform the community as a whole that it is an issue, as you want people to recognize that it will be taken more seriously from this point forward.