An omission in Special Relativity

In Special Relativity there are infinitely many equivalence classes of frames of reference. In each such class every two frames of reference move uniformly with respect to one another. It appears that the following questions have never been asked : 1) In which of such equivalence classes of frames of reference is Special Relativity supposed to hold ? 2) How can we identify such a class, and do so theoretically or empirically ?