Is it safe to do a thread lift on the same day as a fat transfer on the face? If not, how long should it be spaced apart?

One of the plastic surgeons I’ve consulted with is recommending that I do a thread-lift on the same day I do my eyebag surgery and where the fat transfer will be grafted on several areas on my face. My concern is that if my face is swollen from the fat transfer, wouldn't doing a thread-lift during the same surgery after the results in a negative way? Are my concerns unwarranted? And if it’s not a good idea, how far apart should it be spaced?