Well, like the title says, can fishing rods have multiple actions?

Like say it has an extra fast tip, but then the rest of the rod has a parabolic bend?

Or maybe a parabolic tip, really stout section below, and then another really parabolic bend below the really stoutness?

I think I'd be concerned about the integrity of the blank at the transition points.  If the action isn't consistent (or at least a smooth transition) I think it would introduce unnecessary stress points.

No. Action describes where the rod initially bends when load is applied. All rods flex into the butt section with enough force. Even if it were possible, I can't see any advantage to making something like your example.

In multi-piece flyrods you can buy matching tip sections that have faster or slower actions. Power or line size is not affected by changing tips.

Ronnie