The idea came to me yesterday when I got killed by one that I saw the enemy drop. It was dumb of me, I should've avoided it but I was in hot pursuit.

Unlike mines/C4 which arguably are stuck via adhesive, it seems like a frag grenade should be something you can pick up (or even catch) and re-throw, especially given the long cook time. I haven't tried it in game though. Does it work? Would it be cool if it did?