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A serial mass murderer. Not just a serial killer (this is not a serial killing so far, but it is a mass murder). It's really rare in the annals of crime that both occur together - but who knows?
Personal animosity (however unwarranted) with overkill sounds the better of the two choices.
If one types "extensive homicide" into scholar.google.com, there are interesting results. Extensive homicide is when a small group of people (often a family or other cohesive social unit) is killed altogether, or the intent is to kill all of them together.
Serial mass murder is exceedingly rare. I can't think of any, but if anyone finds examples, please post.
(I think you and I are leaning in the same direction). And for people who commit extensive homicide (going from place to place to kill the same set of people - usually family members), there's almost always a record of criminality in the past (not necessarily a felony conviction necessitating being entered into the DNA database though). Sometimes it's minor things, but more often, it's neighbors calling for overhearing fighting or domestic violence that never goes to court, things like that. Public drunkeness, disorderly conduct, etc. Given that most people who commit minor instances of disorderly conduct are ignored by most police, "disorderly conduct" can include things like sucker punching or non-felony sexual assault; the victims refuse to give enough information, but police think it's serious enough to pursue a charge.