Italy stays neutral officially.
If the coup in Yugoslavia still happens maybe Italy makes a secret deal with Hitler and they pull a Poland on Yugoslavia. This gives Italy Dalmatia, Kosovo, and parts of Slovenia.
Allies are pissed, but not to the point of going to war.
Italy ignores Greece and decides to try and mollify the UK and France, recognizing that they pushed the envelope as far as it will go.
Balbo decides to open up Libya for immigration for European refugees. He sees the potential in having millions of Europeans settle in the lightly populated colony.
This gives Italy some valuable PR with the Allies as it gives safe haven to many fleeing Nazi terror.
With Italy neutral, Romania and Hungary decide to sit out on the invasion of Russia. Germany goes it alone.
As a result, the poorly equipped Romanian 3rd and 4th Army is not protecting the northern line at Stalingrad when Operation Uranus kicks off. As a result, the Germans are able to prevent Operation Uranus from being a sucess and they are not encircled.
This obviously doesn't change the big picture for Stalingrad. The Soviets still eventually defeat the Germans. But as they are not able to encircle them, the battle is longer and bloodier as the Soviets are forced to push foward against the German army in Stalingrad itself.
The Russian advance is not as sucessful, but the writing is still on the wall for Italy: Germany will lose.
Italy starts to tilt towards the allies, prompting Germany to invade Italy sometime in late 1943, early 1944.
Allied military aid into Italy and a flood of British troops (coupled with the natural defensive line that is the northern Alps) allow the Italians to halt the German advance early.
A new Stalingrad event occurs in the USSR as the German army in the East is overrun. Perhaps in Stalingrad itself.
From there, the war proceeds much like OTL, except the Italian army is better equiped and acts as a major force in pushing north towards Germany itself. Soviets perhaps don't reach Berlin first, and Italy is able to get major concessions at Yalta.