NN - NN alias "Ternois di Friuli"

Another nice timeline, this one providing a clearer picture of Berengar I's rocky career in relation to the Dukes of Spoleto.

https://www.historyfiles.co.uk/KingListsEurope/ItalyKingdom.htm#Car...

The 2nd one is useful

The last paragraph below gives some context to Berenger having his Supponid wife executed in 915.

Supponids
The Supponids were a Frankish noble family of prominence in the Carolingian regnum Italicum in the ninth century. They were descended from Suppo I, who appeared for the first time in 817 as a strong ally of the Emperor Louis the Pious. He and his descendants were on and off dukes of Spoleto, commonly in opposition to the Guideschi clan, another Frankish family powerful in central Italy.

History
The family consolidated its holdings in northern Italy through the 820s, 830s, and 840s, often controlling the counties of Brescia (hereditarily), Parma, Cremona, and Piacenza among others. Their power was extended and not highly centralised. They shared power with the bishops in the cities and were stoutly loyal to the emperors in order to ensure the peace and stability necessary to rule their vast and separated domains in the Po valley. This loyalty bought them great power, especially in their heartland of Emilia. A Supponid daughter, Engelberga, even married the Emperor Louis II. With her influence, the Supponids became the most powerful noble family in Italy during the two decades of Louis's reign and one of the few to hold high offices.

Following Louis's death, the Supponids supported their relatives, the dukes of Friuli, and the German claimants for the Italian crown against the Guideschi dukes of Spoleto and the West Franks. Their influence declined rapidly after they fell out with Berengar I in 913 and joined the faction of Rudolph II of Burgundy in 922. They are not heard of after the middle of the tenth century.https://en.wikipedia.org/wiki/Supponids