Back in 2002, Greek Culture Minister, Evangelos Venizelos made a proposal for how the return of the Parthenon Sculptures  could be facilitated.
There were a number of aspects to Venizelos’s proposal, one of them being that Greece would offer various other artefacts to the British Museum on loan, in exchange for the return of the Marbles. This would give the museum new artefacts to display, drawing in more visitors, while Greece would get the Parthenon Sculptures back. A win-win situation.
A number of exchanges similar to what was proposed have now taken place in the years since then, Mainly between institutions in the US & Italy .
Past exchanges with Italy involved the threat of legal action, but this one took place entirely voluntarily.
NBC Dallas Fort Worth 
Italy Loans Dallas Museum of Art Installation After Looted Antiquities Returned
Thursday, Oct 31, 2013 | Updated 12:28 PM CDT
The Dallas Museum of Art has agreed to return six antiquities that were looted illegally from Italy. In return, Italy is loaning the DMA an art installation.
In exchange, Italy is loaning the Dallas museum treasures from the Spina necropolis (pictured, above) housed at the Ferrara archaeological museum.
Italy’s culture ministry announced the agreement Thursday. The objects being returned include Etruscan-era kraters — vases — and a pair of bronze shields.
The ministry’s press office said that unlike past negotiations with U.S. museums, which involved threatened or real legal action to recover looted antiquities, Dallas museum director Maxwell Anderson spontaneously offered to return the items after the museum couldn’t determine their provenance.
Italy launched an aggressive campaign a decade ago to retrieve looted artifacts. Its most famous recovery is the Euphronios Krater from New York’s Metropolitan Museum of Art.