When two people are in a relationship that they are extremely unsure about and won't admit anything to their friends about where their relationship is going.
Often times roommates will plan their night around hanging out with their "quasi" so that they won't jeopardize friendships including bromances.
Dave: "Yo Bro, what you up to this week man?"
Brian: "I'm hanging out with the quasi on Monday."
Dave: "Waaa, allright bro I guess that I will plan something with my quasi on Monday so that we can bro-out the rest of the week"