Here is what Mussolini wanted to annex in Africa. Egypt was going to be a puppet state so it isn't colored in. I think the Germans would probably have a lot influence in it as well, maybe more than Italy. The Suez Canal and maybe all of the Sinai was supposed to be directly annexed as well but I think that the Germans would have forced a condominium over it had it been taken.
Mussolini did not intend to give the Vatican all of Palestine, he thought about maybe giving ita few holy sites. This plan was dropped though. If the axis had taken the Middle East I think that Italy would have been given control/protectorate over Jordan and Palestine (and maybe coastal Syria). If coastal Syria had been given to Italy, the rest of it would have gone to Iraq. I think the Germans also wanted Syria and Iraq (with Kuwait) and possibly also the Levant as satellite states for themselves, which is why I'm not exactly sure what Italy would get.
As for the Arabian peninsula, Italy would have gotten control over the southern portion, annexing Aden. Yemen would be an Italian protectorate, as would Oman, which would be joined with South East Saudi Arabia and Qatar as another protectorate. They would also take direct control of islands in the Red Sea.
Here is the max of what Italy controlled in Europe during ww2, and probably the most they'd ever get. Greece was a puppet state (Hellenic Republic), Albania was greatly expanded and in personal union with Italy, Montenegro was a protectorate (in this map it is accidentally part of Albania) Dalmatia and parts of Slovenia annexed, and also shown are the areas of France occupied by Italy after Operation Anton. They also occupied half of Croatia Also noteworthy is that they wanted to create a "principality of the Pindus" out of Greek territory for Aromanians.
Italy also occupied part of Croatia until 1943, the areas left of the black line. You can also see areas they annexed on this map.
Besides that I know that Mussolini wanted Malta, and during the Spanish Civil War Italy occupied Majorica
https://en.wikipedia.org/wiki/Italian_occupation_of_Majorca according to this they also wanted to annex the Balearics and Cueta, a make Spain a client state.