Can I combine ptosis correction with double eyelid surgery?

My Korean plastic surgeon suggested that I might benefit from ptosis correction (눈매교정) in addition to double eyelid surgery. He mentioned that my eye-opening muscles are a bit weak, which makes me look tired all the time. Has anyone combined these two procedures? I am concerned about whether doing both at once will extend my recovery time significantly. Also, will the results look more dramatic than just getting double eyelid surgery alone? I want my eyes to look more awake but still natural. Any advice from people who have had this combination surgery would be greatly appreciated!