The most accepted definition overall is a person who murders more than three persons in a period of more than thirty days.
It's expanded on to say:
Two fantasy driven murders committed compulsively at different times and at different locations where there is little or no relationship between the perp and victim and no material gain is also considered serial murder.
Two or more separate murders when an individual, acting alone or with another, commits multiple homicides over a period of time with breaks of time undefined between each murder event is also, in some instances, serial killing.
Premeditated murder of three or more victim committed over a period of time, in separate incidents, in a civilian context, with the murder activity being chosen by the murderer.
Someone who commits two or more murders with an emotional cooling between homicides.
Someone who over time commits at least ten homicides. Frequently these are ritualistic, brutal and exceptionally violent.
These are the evolving descriptions from the original Bucks and Ressler set-ups from the text when they were developing the early VICAP. They are the principles they sought to link with that first database. A lot of pop-serial killer books correctly site one source and leave the others out, but most of the lit done by Douglas and Ressler that was boring and text like cites the whole shebang.
The time line could technically play out that three murders were committed here.
Murder 1, the mom or the girls
Murder 2. the other from above
Murder 3, the dad
Also, it could have been four
Murder 1. The mom
Murder 2. daughter
Murder 3. friend
Murder 4. the dad
I know the murders all happened separately, but we don't know how much time took place between each murder.
Just saying. Sorry, I usually lurk, but you guys built up like 80 pages on this one. Took me a bit to catch up.