I'm trying to remember why the Italians quit their war with Turkey, and how the ended up with Rhodes ??
Italy occupied the Dodecanese during the 1911-1912 War, as part of their attempt to bring it to a favorable and quick outcome. Thus, the 1912 Treaty of Lausanne stipulated that Italy would withdraw after the Ottomans fully withdrew from Libya - their weakness and the subtle support to the Libyan resistance allowed Italy to keep the occupation up, until the end of WW1 when they got the occupation recognized as annexation.
OTL the Italians nabbed Rhodes and the other Dodecanese during the Italo-Turkish War.
But what if the Turks opted for something a bit craftier? At this point Crete was still nominally under Ottoman Suzerainty and I imagine they could have ceded that suzerainty to Italy in exchange for the Italians getting out of Rhodes.
Italy gets a bigger island that's closer to home.
The problem is, Crete is
de facto Greek since 1908, formally a protectorate of Italy, UK, France and Russia; and for all that Venizelos didn't allow Cretan ministers in the Greek Parliament, they had a keen interest in completing the
Enosis.
So this idea requires Italy to actually occupy an island that is way bigger and more populated, against the wishes of almost every other actor (especially the UK) but Turkey, and their own actions during the Cretan struggle (Italy had been very supportive of Greece until then). A very naked act of aggression.
The hardest part is convincing Giolitti to do it, for the economic and diplomatic cost, and that a swift enough occupation is similarly unlikely; if those happen though declaring 'formal protection of the Cretan State until circumstances change' is a possibility. It also means Greece is way more likely to stay neutral.