Is it possible to do brachioplasty with the twilight sleep?

Technically, yes it would be possible.  However, I do recommend this even though I have had several patients ask.  The reason I will not is because in order to complete the operation under sedation, local anesthetic has to be injected into the arms which causes swelling of the arms.  Notoriously, when doing a brachipolasty, the arm swells tremendously on its own without injecting local and even though the final result is usually as tight as the skin will allow, over the next few days to weeks, the swelling resolves and the tightness of the arm is less than immediately after surgery.  Adding swelling from local would only make this problem worse and make the results worse, in my opinion, long term.  Thus, I think this procedure is best done with the patient off to sleep.  An LMA (laryngeal mask airway) is a nice alternative to an ET (endotrachial tube) in this type of situation so that general anesthetic can still be given without the trauma to the airway.  Best of luck!

If by twilight sleep, you mean deep sedation, then it would be possible, much like some surgeons can perform abdominoplasty the same way.  I don't perform either procedure this way, as I want my patients experience to be a good one and I think having no memory of the surgery and no pain during it, makes for a good experience.  Deep sedation requires the area to operated on to be made numb by injection of a numbing solution.  The injection can be a requirement but can also be uncomfortable for the patient and in spite of the best efforts, some areas may not be made fully numb so can be uncomfortable when these areas are reached during surgery.