I want to start by stating that I'm not an expert by any means like some of the people on this board. That said, there are some things that I have picked up over the years that might help to answer your question.
The Italian military that entered WW2 was a trainwreck waiting to happen. It had so many defficiencies that even Mussolini wasn't blind to some of the problems (as evidenced by his famous quote about only needing a few thousand dead Italians to sit at the peace table). Marathag covered the organization problem pretty well. Other problems the Italians faced were outdated equipment, lackluster leadership, and poor morale.
The Italians were aware of the first problem, and had a modernization program that would theoretically make them a modern military by late 1942 (they had even stipulated in the Pact of Steel that no wars were to be started before 1943). In order to solve the equipment problem you'd really need to either begin their modernization program sooner, not have Mussolini give away a ton of their stuff to Franco, or somehow delay the outbreak of war by another 2-3 years (probably all three, to be honest).
The leadership problem, unfortunately, is unlikely to change as most of the upper leadership had their positions for political reasons rather than military competence. They were largely given their commands either because they were obviously not a threat to Il Duce or (for more distant commands) to remove them from the political scene in Rome. There would have to be some serious (almost ASB) hand-waving to fix that particular problem as it seemed to be heavily intertwined with Italian domestic politics at that time.
The morale problem seems to be a combination of the first two problems as well as not really believing in the cause they were fighting for. Restoring the glory of Roman Empire is great for speeches but it's not something that most people in the modern era were willing to die for. Giving the Italian soldiers better equipment and leaders would go a long way towards remedying this last problem but they would still never have the utter determination displayed by some of their opponents (like the Greeks) since they weren't fighting for something concrete like defending their homes (referring to the initial offensives here).
In short, it would definitely be possible to improve the performance of the Italian military but for the most part it would take major changes to the timeline to get meaningful improvements.