Is there a maximum amount of syringes of hyaluronic acid filler that can be injected and still expect skin to snap back after?

Filler when used properly should replace volume and structure, not overly stretch the skin. The amount of filler used is based on the need of the area and isn't limited per say. If you are worried about skin "snapping back" then it sounds as if the area is going to be overfilled and stretched beyond normal which is not the purpose of filler at all. Please see an experienced injector to be fully evaluated to find out what may be right for your particular situation. 

Hello,  the amount of filler depends on the location. Some of those stars on television have 2-3 syringes of filler in their lips alone while a more natural look is usually around 1-2 syringes.  The studies on Juvederm Voluma (an excellent structural filler designed for the mid-face and cheeks averaged 7+ syringes in the cheek areas (of course they did not have to pay because it was a study).  Around the age of 50, depending on the laxity of skin, smoking, sun damage, volume loss to due bone and underlying fat structure loss simply from aging, many women need 4-5 or more syringes to return the face to a more youthful look.  It really depends on the person and their skin but a skilled injector should be able to direct you towards a natural look.  Also, most hyaluronic acid fillers were designed to be layered on top of one another, so you don't walk out with a "done" or over-filled look.  You can always go back and have additional filler placed.  Good luck.