Is it possible to challenge for a medal after earning it?

I was wondering if it's possible to earn the Celebrity Medal and/or Veteran Hunter Medal again once you've earned it. The reason I'm asking is because back when medals were considered quests, I "completed" these by getting famed like 10 times or killing about 1k monsters and forfeiting the quest, which counted them as complete. As a result, they now show up as a medal I've earned. However, I like collecting medals and keeping them, as dumb as that may be, so I was wondering if I could actually get these medals. I tried talking to the medal NPC but he does not let me challenge for them again.