"whoami" previously suggested custom labels or additional predefined statuses. Along these lines, I would push for a free text field to note a couple of quick details like which security team member is investigating and perhaps a service ticket number from our help desk.
A strict "assign to" of an existing user could be better though as that would be easy to use as a custom filter for the CVE list.
I would also suggest being able to apply the ignore option to individual assets under each CVE as we clear them or find that is a false positive for that asset. Perhaps ignoring the CVE at the top level would mark all currently identified assets as "ignore". This way if another asset later matches on this CVE it is not overlooked. It may not be a false positive for that added asset.