When one checks in online, Delta now asks how much money in travel vouchers it would take to get you to voluntarily give up your seat and be bumped to another flight. Suppose what I'd really like isn't travel vouchers but rather an upgrade to first class. Is it possible to request something like that? Even better, is it possible to say, I'll take either $X + an upgrade or $X + $Y?
There's currently no standard way to request that a portion of your compensation be a first class seat on the new flight you're bumped to.
My speculation is: requesting this would involve talking to the agent at the gate inside the airport while they find you a new flight. At that point you could offer to upgrade to first class if a seat is available. Doing this beforehand online is hard since the airline doesn't know which new flight you will agree to.
If you mean you want to be placed in first class on your current flight instead of being bumped to another flight, I believe that can't happen because your current flight is already 100% full.