With regard to Gerhard's response -- which I agree with -- I see a number of things problematic in some of the behavior taking place in the present circumstances.
I have no doubt that behind these numerous accounts is only a very small group of humans, and there's a very good chance it's just one. In other words, I am finding very clear evidence, using the moderator tools available to me, of sockpuppetry taking place. As you all know, sockpuppet upvoting is a significant violation of site (and SE) policy, but sockpuppetry is obnoxious for other reasons as well. In the present case, there have been numerous instances of the sockpuppets' answering each other's questions, editing each other's posts, and leaving comments on each other's posts. Even in cases where no sockpuppet upvoting is taking place, an appearance is trying to be created of great community activity and interest surrounding the posts in question. This type of attention-drawing is based on deceit, is thoroughly obnoxious, and is inherently problematic.
I think the behavior promised in this user profile https://mathoverflow.net/users/141500/human-path?tab=profile also qualifies as problematic:
The Six Paths of Pain are controlled by Nagato. The Six Paths of Pain do not answer, upvote, comment on each other's posts. The Six Paths of Pain award bounties on each other's posts.
Judging from this post, it seems that Community Management agrees this behavior is not cool: https://meta.stackexchange.com/questions/37096/who-or-what-is-this-so-user
Still other problematic aspects include opening new accounts in response to other accounts being closed. In one case relevant here, an account named "mika" was (re)created after a same-named account was deleted, with the user openly saying so. Deletion can mean one of several things. One is that Community Management or site moderators have decided that the user is no longer welcome, in which case the user opening a new account is explicitly in violation of community moderation. Another is that the user is self-deleting the account voluntarily. But in this case as well, coming back again in a new form flouts the norms of this site, especially by enabling the user thereby to evade community moderation and policing. This is akin to question repetition, as when a user deletes his post and then asks again.
Still another problem -- more of a judgment call but nonetheless real -- is trollish behavior (sealioning, etc.). In my opinion, and in the opinion of other community members, there have been a few instances of that in the current circumstances, both at meta and at main.
In such cases, when the behavior becomes problematic and repeatedly so, we may have to clamp down a little harder. (Many of you will remember one or a very small band of users engaged in shenanigans a few years ago, with the main perpetrator now permanently banned from SE.) I don't have a problem per se with a user controlling a number of accounts -- as long as site policies and guidelines are not being flouted and deceit is not taking place. Otherwise I have a big problem with that.
I guess I'll begin documenting here suspicious events as I see them. For those users who seem puzzled about my linking certain posts on MO Main to this discussion, I repeat: forensic analysis strongly suggests to me that all of the many accounts listed above are associated with each other, and I think the community should be aware of events that are occurring within this circle.
For those with 10k+ reputation: the (unregistered) user "Curious girl" asks a spam question https://mathoverflow.net/questions/333692/big-topos-guys-why which makes a crude joke about genital size.
User "cardinal" https://mathoverflow.net/users/74900/cardinal has the following recent reputation events https://mathoverflow.net/users/74900/cardinal?tab=reputation: yesterday there are 5 upvotes in the same minute 20:14, and 4 upvotes in the same minute 16:26. Today (June 11) there is a slew of upvotes all within a short span of time.
A number of accounts in this circle that are offering bounties follow a characteristic pattern where coincident with offering bounties, the account is scheduled for deletion. This will continue until past the time of deletion, and then the deletion will be rescinded.
A new version of Asura Path became a member today https://mathoverflow.net/users/141752/asura-path?tab=profile, after a same-named account was self-deleted. This self-deletion plus resurrection may be an attempt to circumvent ordinary moderation. Here is a list of posts by the old Asura Path: https://mathoverflow.net/admin/posts-by-deleted-user/141498