A harder line Communist Party is the easiest way.
However, the worst Italian war crimes were committed 1) before the war, when the Fascist regime was seen as a legitimate partner by the winners 2) largely against not-quite-white-skinned people in Africa who had relativaly little in the way of tools to make their voice heard internationally, in the context of the same colonial "policing" France and Britain were still very much busy undertaking (although thankfully without poison gas, unlike the Italians).
The Italian crimes committed against "civilized" people, while still very nasty, were indeed pretty tame in comparison to what the Nazis and the Japanese had performed.
So, at the international level, the pressure was very limited.
An "internal" Norimberga (trials solely by Italian authorities) would have been possible is the Communist party and others leftists had pushed for that (IOTL they chose not to). The problem was that it was (quite rightly) seen as traumatic and thusly counterproductive to the essential aim of getting back to normalcy as the speediest possible pace.
That of course fostered the extremely dangerous myth that Italians were "good people" that only did wrong thing when forced by the evil Nazis, which would indeed be sort of true if Libyans, Ethiopians and Yugoslavs weren't people, too.
(I have not mentioned persecution and destruction of Italian Jews, because indeed it happened under Nazi urge. But it found quite a willing response. Contrary to widespread belief, Fascism did have an Anti.Semiic streak right from the start, although it took the Steel Pact to become dominant. )