OTL, Italy received assurances at the congress of Berlin from France and the other powers for "compensation" in tripoli. In practice, they failed to make use of these assurances until 1911.
One reason for that is that between 1884-1895 (when france took Tunis), Italy was engaged in a struggle for control with Ethiopia which ended in a disastorous defeat for Italy in Adowa. This defeat was sufficient to give colonial adventures a very bad name in Italy for some time.
What if, for whatever reason, Adowa, and possibly the Italian occupation of Northwestern Eritrea, is avoided? Say better ethiopian-British relations lead to Britian keeping it's word and having Egypt hand Massewa over to ethiopia when they withdraw. Say the italians are compensated with renewed reassurances for their sphere of influence in Libya (and maybe more of Somalia).
Crispi's government is still in place when the Greco-Turkish war of 1896 starts. If he tries to use the opportunity to invade Libya in the same pig headed manner as occured OTL in 1911 (demanding annexation instead of the Anglo-French version of informal rule in Tunis and Egypt), does Abdul Hamid give in without a fight?
If not, does Italy try to force him to capitulate by aiding the Greeks or landing in Albania?
Do the Slavic Balkan states join in?
If the fighting goes on for too long does Macedonia erupt in rebellion?
Does the Austro-Russian agreement for maintaining the statues quo hold?
Does Russia maintain a focus on the far East?
Might Austria threaten actual war on Italy, counting on it's agreement with Russia and alliance with Germany to give them a clear hand to revenge themselves on the house of Savoy?
How much strain can the Crispi government take before it collapses?
Who does Germany choose to support? Can Willhelm II organize a third congress of Berlin to end the conflict to Germany's advantage or is that beyond his diplomatic skills?
How concerned are the Austro-German and Russo-French blocks about wooing Italy into their respective alliance system?
Does this have the potential of developing into a very early version of WWI?
What is the red line for each power which will cause Britain to intervene?
How much will each power respect this red line?
OTL, the great powers tried to bring the Italian-turkish war to a swift end before the balkan states got riled up and declared war on the ottoman empire. they failed, which is why the ottoman empire eventually gave in to Italy. TTL, a stronger OE is already at war with Greece (which it is handily beating) when Italy invades Libya. Where does it go from here?