It is possible if you’re willing to use your own form with your own code:
Create a repeater of avatars (or popup with such a repeater) and let the user either chose an avatar or alternatively upload an image. When the user chose either of them override the previous image url and use the avatar url instead.
https://www.wix.com/velo/reference/wix-members-backend/members/updatemember?_gl=1164j6w8_ga*NDQxNDY5ODQyLjE2Mzk0MDE3ODY.