It's possible. You'd have to set up a temporary roof first to cover you as you work on the real roof. That temporary roof could simply be a very large tarp.
In general the advice is /don't do it/! You'll end up sandwiching moisture between your house and the roof. If not dried properly this will cause mold and increase leaks.
It's possible, but no one does it. Notice how the construction guys call it a day when it starts to rain? There's a reason for that -- you're asking for trouble if you erect a roof in the rain. Don't do it. Just wait til it clears up.
It's possible, but it's not recommended. No mater how careful you are and what temporary roofs or tarps you erect, your materials are more likely to be damp and affect the structural integrity of the building.
