So, I think the first thing to highlight is that the relationship Hitler held towards Stalin was of a very different nature to that of Mussolini, meaning that attitudes were also very distinct.

Firstly, let's consider Hitler and Stalin. To say thay Hitler "turned" on Stalin perhaps suggests a greater level of mutual trust and comradeship than existed. It also reduces the complexities of the two regimes to the two dictators that topped them. Whilst, of course, Hitler and Stalin are crucial figures when considering the historical events of the period, they were not the sole players and both regimes had complex, and often deeply divided, institutions of power. Consequently, when Hitler and Stalin formed the Molotov-Ribbentrop pact, it's worth remembering the number of other actors involved in the decision and details, most notably the namesakes of the pact. Furthermore, it's important to note that the pact was not a deep commitment that both sides deeply believed in, but a political screen that, at that very specific moment in time, benefitted both regimes.

Stalin was very aware of the dangers that Hitler presented the USSR, and the agreement helped provide him more time to reorganise the Red Army and internal political structures so damaged by the Purges. For Hitler, the agreement helped secure the Eastern Front in the short-term so he could focus on the seeming juggernaut of France and Britain. There was, however, no way in which Hitler viewed the agreement as anything more than a tool. Hitler despised the Slavic people, the Bolsheviks, and, as per, the Jews that he believed were intrinsically linked to these two other groups. The Pact was calculated international politics, and its ending was less of a shocking betrayal (despite Stalin's personal difficulties in accepting how soon the break came) and more of the launching of Hitler's self-imagined and fanatical crusade against the Bolsheviks.

I know that's a lot on only one side of the question, but it's worth laying out as it helps demonstrate the very different relationship that Hitler had with Mussolini.

On a personal level, Hitler knew Mussolini to a much greater depth. In the early days of fascism in power, Hitler viewed Mussolini with respect and certain admiration - here was a man leading a national regime in a fashion similar to Hitler's ambitions. However, as Hitler's own power grew in the mid-1930s, his respect for Mussolini steadily fell. This was a combination of, as ever, racial imaginings of Italians, alongside the fact that Hitler increasingly found Mussolini indecisive and ineffective. Hitler was a huge gambler who took massive risks against the European superpowers - Mussolini's biggest military movements were against Ethiopia, a comparatively weak nation, and from there the Italian army famously faced protracted struggle and defeat from Africa to Greece. Fascism has a strong strand of 'might is right' within it, and Hitler especially embraced the idea of 'eternal struggle' - Mussolini did not represent this to him.

Now, from this it may look like therefore Hitler would be interested in betraying Mussolini, assuming an alternative timeline now (which is always a perilous, but entertaining, strand of investigation). However, this requires an assumption that Hitler was, by nature, a man who would ALWAYS take the move for greater power and deception, regardless of the direction. Whilst I would certainly evaluate Hitler as an untrustworthy bastard, it's again worth remembering his worldview of being the 'saviour' and 'conqueror' for the Germanic peoples over Jewish Bolshevism. His fate was in the East, in building greater Germany and enslaving the Slavic population. The South of Europe was, in comparison, lacking in interest to him. It was comparatively underdeveloped, lacking in natural resources, and populated by an 'inferior' but not necessarily an 'enemy' race. Consequently, whilst Hitler would be interested in the power balance of Southern Europe (as shown by his commitment to keeping Mussolini in power, though this was mainly down to military concerns as the Allies pushed through Italy from 1943), whether he would have gone so far to invade it, for no real gain or reason, is deeply questionable.

This can be reinforced when remembering that Hitler's involvement outside of Austria, Czechoslovakia, Poland and Russia (the areas of Europe he viewed as either Germanic or to be a Germanic colony) was almost always out of military 'necessity.' He only went to Africa and Greece because Italy needed support. Yugoslavia presented a threat to his rear lines invading Russia. Scandinavia was conquered to deny Britain invasion routes. France was invaded, yes out of revenge, but primarily because the West had to be secured in order to conquer the East. The story of Hitler is centred on Ruasia, and thus everything else must be viewed through how it contributed to this overarching goal.

In short - Hitler less 'turned' on Stalin and more simply fulfilled his political ambitions. Italy did not offer similar importance to his worldview and offered few material benefits. Consequently, it is doubtful Hitler would have turned on Mussolini. Hope that helps answer the question!

My main knowledge of this comes from the following that I can think off the top of my head:

Hitler - Ian Kershaw - (deep dive on Hitler) The Third Reich - Michael Burleigh (deep political, social, economic)

More 'popular' history books: Dictators - Frank Dicotter (Broad political) Armageddon - Max Hastings (military) Stalingrad - Antony Beever (military)

Plus then various political works on what constitutes fascism etc (George Orwell has some interesting general writing on this, and looking at Spanish fascism provides interesting comparisons and differences to the Nazis), alongside bunch of documentaries over time.

I haven't specifically cited each thing I've written here, it's the generalised themes and facts I have, so if I've gotten anything wrong or simplified anything too far, feel free to correct with citations!

In short, no. Hitler saw Communism as fundamentally evil and an enemy that needed to be destroyed. He made no attempt to hide this thinking as it was one of the most commented subjects in his manifesto. In addition Hitler believed in German racial supremacy and the racial inferiority of the Russians, Belorussians, Ukrainians, and Baltic peoples. Hitler's ultimate plan was for Lebensraum (living space) in which Germany expanded to colonize these "lesser" nations to exploit their resources and cheap/slave labor while exterminating the "lesser" peoples.

Hitler did not have these same feelings and plans anywhere else. In a "perfect world" for him, Germany would be at "peace" with France and Great Britain, establishing puppet governments to colonize and exploit their populations but leaving governance of the scraps left to their people.

Hitler and Mussonlini were in agreement on fascism but their relationship was very one sided, dominated by Hitler. Their alliance was strictly political/symbolic as Italy's military had very little to contribute. While Hitler at many times became very frustrated with Mussolini, he continuously wrote him expressing admiration and even later sent a daring and successful rescue mission after he was overthrown in Italy.

So while Hitler would undoubtedly had no problem turning on Mussolini if he were to openly oppose and take up arms against Germany, it is not even in comparison with how inherent Hitler's hate for communism and the people of the Soviet Union was. Invading the Soviet Union was at the front of his mind ever since he came to power.