I'm mainly indifferent to serial killer OCs since so many of my OCs fall under the term 'serial killer' (The term applies to people with three or more kills, but there's a lot of disagreement and all that but we'll just use this definition for the term for now)
It honestly depends on the universe your OC resides in! Let's take my OC Yukari in my Liar Liar universe for instance. She is a serial killer, with 10+ confirmed kills. Obviously this is ridiculous, impossible, and she'd be caught and trialed immediately since the kills were all confirmed to take place at the same school, and not only that, several people (Nao, mainly) have known about the murders, but didn't care enough to intervene... The Liar Liar universe is almost a parody of the world we live in, in the fact that there is literally little to no rules, and is a world where people are born with naturally blue, green or pink hair naturally.
On the other hand, my magical girl universe follows more "real world" rules, as in, anyone caught killing will be caught, trialed, and/or executed! Killing, murdering, is heavily looked down upon and mostly how people feel about in universe are similar to our own. Whether you feel your OC in particular is "going overboard" really depends on the rules set up in your universe.
Think about your "in-universe" rules. Do you feel it is unreasonable that this OC is getting away with 3 or more murders? Do you feel it is necessary that this OC go around killing people? Why are they doing this? The more unreasonable reason for killing is, perhaps you should tone it down. (Keep Disproportionate Retribution in mind:
http://tvtropes.org/pmwiki/pmwiki.php/Main/DisproportionateRetribution) Remember, while in real life not all people have a reason for doing what they do, it's a hard and fast rule that most of your OCs should have some type of reason for doing what they do....
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