Italian strategy after controlling the Mediterranean

What should Italy do if it controls Malta, Suez, Gibraltar, and East Africa by late 1942 and has Aquila available?

It should secure the new internal sea route, build carriers and cruisers, and turn the Mediterranean into a dependable logistics corridor toward the Middle East and East Africa.

The hypothetical begins with Aquila in service, Malta and Gibraltar captured, and Italian East Africa still holding out; control of Suez is added to the premise. That would give Italy an internal Mediterranean line of communication and an opportunity to advance toward the Middle East. Additional carriers and cruisers are proposed to secure the territory and keep supplies moving. Those gains are accepted for the design exercise, although capturing Malta without destroying much of the assault force remains in doubt. Holding the conquests creates an immediate requirement to protect the routes connecting them.