As a followup I suppose retaining Savoy could be quite helpful, if only for the coal there. Italy had very limited coal reserves of it's own, always a bottleneck. I haven't read much Italian economic history in a while, but my understanding is that a big part of the problem is that Italy came quite late to the game. So like before an earlier unification, with somewhat greater access to resources, could create the synergy needed to push Italy up to Great Power status a decade or two before it did OTL.
The other big way to do this is to nerf the other European states. So for a *very* rough sketch, say Italy does manage to do a bit better in the 19th century, well enough that it satisfies its major claims on both France and Austria. Then comes a major European war with roughly the same lineup as OTL's WW1, while Italy remains neutral. Germany&Friends win, with France ending up neutered while Russia loses some border territories like Poland but does not collapse like in OTL. Britain gets a white peace. Italy generally makes some money during the war, though not as much as one might think given that even a stronger Italy during the early 20th century will still be very dependent on a global trade network that has been terribly disrupted. Nevertheless Italy does ok, and most importantly is entirely undamaged during the war. Post-war it has by a good margin the most powerful fleet in the Mediterranean.
To continue the OTL resemblance, let's say there's a rematch 20 years later. In the mean time Germany has been enjoying European hegemony but nevertheless Britain and Russia with a weakened France present a major threat. Russia in particular has industrialised, and for arguments sake is some sort of reformed Tsarist thing that resembles OTL's 1914 Kaiserriech in its political makeup i.e. a bit democratic with lots of power still remaining in the hands of the monarch. Queue 'WW2', Germany manages to do very well in the west knocking out France but is involved in a terribly bloody conflict in the east which appears intractable. To try and finish affairs in the west it attempts to invade Britain, with further buildup between the wars Germany has a moderate naval advantage over the UK and manages to knock out the Royal Navy and lands in South East England. It is unable to defeat the British quickly however, creating a bloody and destructive conflict that ruins large parts of the country's most urbanised region. Meanwhile Russia has begun to gain ground in the east, and has begun invading Germany proper. Berlin falls, perhaps as much as the entirely of OTL East Germany/lost Eastern German territories are overrun. At this point Italy, not wanting to live under a Russian dominated Europe, intervenes on the German side while ensuring that Britain is given a white peace. After 6-12 months of fighting the exhausted Russians retreat from a ruined Germany, and for good measure have some political upheavals to keep them busy.
So here we have a situation in which all the major European powers have pretty much wrecked themselves except for Italy, which can claim the role of 'saviour of Europe' from the Russians. None of the European states can claim continental hegemony in any sense whatsoever, and for fun Italy can also be the most liberal/democratic of the bunch.
A very very rough sketch, probably pushing the OTL-allegory a bit too hard in places, but overall the point is that in 20th century Europe just staying out of the destructive wars is a sure fire way to improve one's overall position, so long as none of the fighting countries can claim the whole pie. The US did this of course, going from first among equals to lonely at the top thanks to all its rivals ruining each other. Italy could never be the US, but it could certainly do a smaller version of this. So probably could Britain or Russia, depending on the scenario.