Thank you!
If quest is based on a stencil, you can take the same stencil for yourself.
Otherwise, it's a feature called "Cloning", and it's not implemented yet: http://questhub.io/realm/meta/quest/51f7ab8688a70b5f74000046
About 10 minutes after I posted this, you commented on one of my Quests and ended up turning it into a stencil, thus answering my question before I got back here to read your actual answer!
It's a neat idea, I'll have to check out the meta-quests.
I expected to be able to attempt other peoples' quests, but I don't seem to be able to. Is that outside your scope, just not implemented yet, or am I simply missing it?