  An entanglement witness is an observable detecting entanglement for a subset
of states. We present a framework that makes an entanglement witness twice as
powerful due to the general existence of a second (lower) bound, in addition to
the (upper) bound of the very definition. This second bound, if non-trivial, is
violated by another subset of entangled states. Differently stated, we prove
via the structural physical approximation that two witnesses can be compressed
into a single one. Consequently, our framework shows that any entanglement
witness can be upgraded to a witness $2.0$. The generality and its power are
demonstrate by applications to bipartite and multipartite qubit/qudit systems.
