posting questions that they know are not in line with the intent and purpose of this forum
That might be another or a separate problem, i.e. if a question is bad then it hardly matters which account was used to post it.
Is this something that is within the bounds of how this site should be used?
The slang word (i.e. the jargon) for an alternate account is a "sock-puppet" (so-called because it looks like a separate/independent user but it's not autonomous, instead it's controlled by someone else).
A reason why some users create sock-puppet accounts is to up-vote themselves: that's a standard problem, and there are automated mechanisms in place to detect and prevent it.
This answer says that the following, too, ought to be seen as problematic behaviour:
- Answering your own questions with the other account(s)
Is there a way to contact the site administration to confirm that these accounts are coming from the same source, should it be determined that this behavior does undermine the spirit of the site?
One way is to 'flag' it for moderator attention (when you flag it, choose the "other" reason at the end of the list and explain the problem clearly).
And/or let a moderator know that you want us to contact you privately so that you can explain the problem (e.g. post a little comment in reply to any of my posts, saying something like "@ChrisW can I have a word with you in private?").
And/or you can contact the site administration (the SE community team) using the contact page (there's a link to this in the footer at the bottom of every page).
A communication like this from you, to the moderators or to the SE team, would be handled confidentially.