In "chapter 5" the basis of the device is revealed to be the "activation" of DNA. The "active DNA" is why things grow so fast after changing and grow back if they are tampered with. It is DNA actively making the cells carry out it's instructions instead of being mostly passive after initial development of the organism like regular DNA.
Example: if we cut off a finger why does the finger not grow back if our DNA has programming for that finger? With active DNA the body would continuously grow back and maintain the shape and function of whatever it's programming is.
The only reason I put the "one change only" in the initial letter was really a plot device to make the changes more permanent and to have more variety within any given area. I didn't want people with "bad" changes to be able to wander around getting "better" changes and I didn't want a diverse environment like the campus in chapter 3 to be "flattened" by a blanket change later on.
In chapter 5 the device is shown to be able to "ping" a person's DNA/basic cellular makeup. The five have the device set to autoreject any "active" DNA it reads back. There is nothing physically stopping the five from doing multiple mods, in fact they use it on themselves repeatedly to hide. They also do a couple multi mods in chapter 4, "The I-Files"
That being said once a branch leaves the tree it belongs to whoever is writing it, you are free to make up your own rules!
Thanks for branching the story!