On Stack Exchange, there is no rule against a user having more than one account so long as the extra accounts aren't used to cheat (sockpuppet voting and the like). In fact, on some sites it might be a good idea to create a separate account to ask a question that you don't want to have linked to you directly. That's all fine.
On a site I moderate, we have a user who has created several accounts, each of which has been used to ask several low-quality questions. A single account asking that many low-quality questions would have been suspended, but these are distributed so no individual account has reached the threshold. If those questions were all piled up on one account then the pattern would also be more obvious to community members, but what usually happens is that people see a poor question from a "new" user, try to help out with edits, tutoring, and even answers, and later realize their effort was ill-spent. In one case an active user seems to have figured out that two different users are the same person, but mostly this isn't discussed.
I'm pretty sure that the user is quite intentionally spreading the questions among accounts; this isn't a case of accidentally creating new accounts. As a moderator I can see private information about the accounts, which is how I know (99.9%) they're the same person, but site rules forbid me from publicly identifying the group as the same person.
We have spoken individually with some of these accounts about quality, but the quality has not improved. We have not, so far, spoken with any of the users about the multiple accounts.
This person isn't technically breaking any rules, but is nonetheless becoming a small drain on the community. How should I and my fellow moderators respond to this before it becomes a big drain? Should we try to talk with the users, be more aggressive in deleting poor posts from these users (where others would get more leeway), something else?
I'm aware of How to handle a disruptive user who doesn't break the rules? but the disruption there is more evident so the answers are probably different.