overlapper 

One who fails to break up in a current relationship before starting a new one.

or if you are from Massachusetts... ova-lappa

"Fran is an overlapper. Afraid to have the awkward breakup talk after they have found another lover."

overlapper by HBombD June 30, 2017

Overlapper 

Someone who is always in a relationship. They can't stand being alone so they have the next person lined up before breaking up with their current fling.

Dang! Jason just broke up with Lilly a minute ago and is already out with his new girlfriend, Amy. Oh you KNOW he's an overlapper!

Overlapper by TypeJ January 15, 2016

overlapper 

A person who isn't "quite done" with one relationship before they start up another. This person does not refer to themselves as a cheater because "they were getting around to the breaking up part." They also don't consider themselves codependent, even though they can't stand the thought of being single for one bloody minute. Technically, however, they are both.

I'm not that picky about the women I date; I don't care if they're divorced, or if they have kids, or if they have a bunch of kids, like more than two. I just don't do liars, cheaters, or overlappers.

overlapper by Banter2012 December 28, 2015