There have been already threads on this, but not recently, so I will try to propose again the following POD:
Instead of giving just 24 hrs of ultimatum to the Ottoman Empire, the Kingdom of Italy adopts a more conciliatory stance, giving a ten-days ultimatum on the Libyan question. During this time the OE proposes a "Tunisian" suolution, so basically giving powers of administration and de facto rule over Libya to Italy, in exchange of an indemnity, while retaining formal sovereignity over the area.
Giolitti accepts, maybe because someone shows him more reasonable extimates on the costs of war.
What are the consequences? Can the Balkan Wars and maybe even WW1 as we know it be butterflied away? I doubt it, but maybe it could be slowed down, taking place in 1916 or so.
Italy would be better off, although without the Dodecannese, but not much, because I expect them to screw up relations with the local tribes and end up facing a prolonged guerrilla. What is more interesting is that there should be less militarism, and possibly the Socialist Party might stay united and closer to power together with the Catholics.
Relations with Turkey would be better than in OTL obviously, which might have some impact if/when WW1 starts.
In short, this could be a way to have a more democratic Italy in the first half of the XX century, what do you think of it?