I apologize if this is inappropriate and will gladly delete it if so.
I'm not really taking about the Caligula type, but what we refer to nowadays as serial killers. Do we know of any and if so, what are the stories behind them? If not, what are the earliest known serial killers throughout history?
So, there are going to be some problems giving you a satisfactory answer on this, for reasons I will get into below, but the short answer is 'while we can speculate that they probably existed, the concept of a 'serial killer' is a modern one, and most ancient societies lacked the kind of jurisprudential records or study of what we now call 'criminology' to make the kinds of connections that would be necessary to prove it to a modern standard.'
The history of criminology as an academic study is a very interesting one, but it's not my particular area of expertise, so I might instead invite you to ask a specific question about that or do some further research on the subject, as it's all very riveting stuff.
Now, as for some specific examples that might fit the definition of 'spree killings' or at least 'multiple homicides', a few come to mind from the classical period:
Titus Livy, in The History of Rome, tells us of a group of 20 women who were found to have engaged in the poisoning of several prominent Roman citizens in 331 BC. When discovered, they were brought before the forum and asked to drink the draughts they had been found with. They agreed, and all died within minutes. (Book 8, Chapter 18)
The Book of Han contains the story of Liu Pengli, Nephew of Emperor Jing during the 2nd Century BCE. Liu was known to rampage across the countryside with an armed escort at night, terrorizing and often times outright slaying the villagers and particularly slaves they came across. (Volume 5)
Perhaps closest to the modern definition, though one of the more poorly sourced, Zu Shenatir was (allegedly) a wealthy merchant who lived on the outskirts of Aden, in modern-day Yemen (then Ḥimyar). He was said by the local people to lure young boys to his home, often plying them with offers of food or money, before sexually assaulting them and throwing them out of the highest window of his home, usually to their deaths. (The Human Predator: A Historical Chronicle of Serial Murder and Forensic Investigation, Katherine Ramsland)
Hopefully this can at least give you a bit more to jump off from in your own research.