I think the only rights that can be "common" to all are those unalienable individual rights held by each and every person. Beyond that, I think the term "common rights" has the tincture of group 'rights' which is also a fiction.
How are "inalienable individual rights" any less of a fiction than "common rights"?
If one looks at the human condition through the lenses of history, anthropology and biology, the claim that we have any natural rights, individual or collective, appears to be preposterous.
I hold to the distinctly unappealing view that we have no rights whatever --- only duties!
More seriously, it is obvious that any rights which we may be said to possess, individual or group, are fragile constructs which arise through difficult, sustained collective effort --- and not a little historical accident!