I attempted to explore a hypothetical situation a few weeks earlier where it was questioned how Italy would fare in the war with Mussolini having died shortly after Italy's entry. Now I would like to try something different:
Lets assume that on the brink of the collapse of Paris Mussolini decides against entering the war. Although historically he intended to only have a few hundred dead for a seat at the peace conference, perhaps in this timeline the unprepared state of the Italian Army is impressed upon him a little more and he reluctantly opts to sit it out.
At first he will breathe a sigh of relief because Britain, contrary to all expectations, does not surrender post the Fall of France. However Mussolini is a very opportunistic kind of guy, and while he might initially be happy with making a lot of money from being neutral, it seems likely that at some point he would want to join the war. It's also possible that he may always feel that Italy's entry in 1940 might have been enough to tip the scales to force Britain's surrender (obviously false but it's something he might believe).
So what if later on Mussolini, after watching the stunning progress being made in Russia, is determined to enter the war when it seems like German success is certain? This might be in the third phase of Barbarossa around October 1941 when Russia is at their weakest. Does the extra year and a half of preparation allow Italy to perform more competently? Will they have benefited from observing modern warfare in action and use the time to drastically implement doctrinal change?