There is no attempt at plausibility, there are no logical premises for the fictional speculation, it just dumps the viewer into a bunch of stereotypes.
Trinity Seven is absolutely trashy wish-fulfillment.
I plan to watch every episode.
The ending credits flash the Latin names for the Seven Deadly Sins. Obviously the one girl wearing lingerie and short-shorts is supposed to be Lust, but I wonder which one the redhead is supposed to be – Pride or Wrath? And the emotionless girl in the bath is probably Sloth.