This is called "double clutching." It is common practice, and it USUALLY is okay for proven pairs. However, it is not as safe as only doing a single nesting. Every time that a budgie raises a clutch there are risks, but it gets worse with each back to back laying. It DOES take a toll on their body. I have no knowledge about the correlation between multiple clutches and egg binding: I have never had a hen suffer from this. My worry is about the toll on their bodies. Any mother gives resources from their own bodies to create their young, humans and budgies included. Sometimes, hens can die of malnutrition and exhaustion from bearing too many clutches. Males can become sick from the stress of having to vomit up the majority of their meals each day to their partners.
So long as they are provided with everything that they need, they can make it through this "double clutching" process okay, and recover the lost weight and nutrients after the second clutch. I don't endorse this because it has been proven to effect their longevity. Ideally, people should breed their budgies once a year only. Unfortunately, most breeders have to think about buisness as well as the care of their birds, and will double clutch. In fact, I have found more breeders that double clutch than those that do not.
If my own birds laid a second clutch before I could remove the nestbox, I would allow them to keep it. However, a third time, I would take the eggs from them. Their safety and health comes first, and three is just way too many. A fourth clutch might have been the end of this poor little hen.