Pardon me please, but I believe it isn't the back part of a 2- or 3-piece button. If it was, the raised rim would be pointing away from the side with the backmark. See the drawing below, from the Albert button-book. So it's a 1-piece button, though a rather strange one. There are some late-1700s-to-early-1800s British/American brass 1-piece buttons whose backmark is a circle of "raised-mark" stars with some intervening punctuation. One example is Albert-book button NA-17A, an early US Navy brass 1-piece button. Its backmark is simply 12 six-point "raised" stars.