oneupsetmanship 

A specific variant of oneupmanship whereby two people compete over who upset whom the most. This process can spiral out of control when successive descriptions of why one party is upset causes the other party ever greater upset, thus passing the upset back and forth until upsetmageddon is achieved.

Jack and Jill started an argument which rapidly turned into oneupsetmanship

oneupsetmanship by Nigeywigey June 15, 2018

Oneupsmanship 

noun. The act or quality of being better, i.e. to "one-up" another. Someone with highly honed oneupsmanship is able to easily, elegantly and constantly one-up those around him or her. Frequently viewed with hostility and suspicion by those with poor onesupsmanship. Can lead to arrogance and condescension if overused.

Person A: I just bought a new car! It has a V8, it's so fast!
Person B (exhibiting fine oneupsmanship): I'm sorry, what were you saying? I was just polishing my Enzo Ferrari and I didn't hear you.

Oneupsmanship by we@y April 6, 2009