  We prove that any multiple-copy entanglement transformation [S.
Bandyopadhyay, V. Roychowdhury, and U. Sen, Phys. Rev. A \textbf{65}, 052315
(2002)] can be implemented by a suitable entanglement-assisted local
transformation [D. Jonathan and M. B. Plenio, Phys. Rev. Lett. \textbf{83},
3566 (1999)]. Furthermore, we show that the combination of multiple-copy
entanglement transformation and the entanglement-assisted one is still
equivalent to the pure entanglement-assisted one. The mathematical structure of
multiple-copy entanglement transformations then is carefully investigated. Many
interesting properties of multiple-copy entanglement transformations are
presented, which exactly coincide with those satisfied by the
entanglement-assisted ones. Most interestingly, we show that an arbitrarily
large number of copies of state should be considered in multiple-copy
entanglement transformations.
