<p>Ideally the main issues should be addressed when it is first closed (I often comment when voting to close for one reason with a brief mention that a post would close for other reasons as well -- something like "not only is this unclear, it appears to be overly broad..." etc), so that the OP is aware of the main problems to address.</p>

<p>My preference as a moderator when one problem it was closed for is fixed but other issues may remain is to open the post and re-close under the new reason (preferably with a comment to make the reasoning clear).</p>

<p>This is not always practical without a moderator (since the reopen may not succeed and even if it does the new close may not); I think a comment is a reasonable way to let the OP know that the question either may need additional editing to be on topic for our site or (if they prefer) should be flagged to migrate to a more suitable location.</p>
