Mark Job as filled by Person applying

I am building a job board for a local Santa group. This plugin provides a LOT of great things for this group, the only downside to how this operates and how the group generally operates, is in how jobs are shown as filled.

I am envisioning a site where, using the honor system, a job can be marked as filled by a Santa (or the job poster), and mark who has taken the job. This would be an honor system, where we all trust that we are doing this for the children. (This is largely how their current system works, however EVERYTHING is over email, so there is no way to truly know if a job is filled or not.)

Is this possible?