McBride sharpens his tough-guy image (think: “Parks and Recreation’s” Ron Swanson with a bad marriage and a nasty streak); Goggins takes his “Justified” persona and gives it a velvet lining.

The two are perfect together, calling each other out in the teachers’ lounge; sharing a private moment in the woods near the school.

When “Vice Principals” turns to their home lives, we get one more layer and a bit more insight into their actions. Goggins, again, is a revelation, able to make one more character as indelible as his last. He flounces around the school like a picture of sweetness and light, then plots dastardly deeds in the darkness of his home.

To push the buttons, Brown brings in an “observer” who plans to watch how the school runs before making suggestions. Naturally, both vice principals are convinced he’s there to end their jobs. Russell gets secret intel on the principal; Gamby suggests an on-site visit to her home.

While “Vice Principals” escalates in ways you couldn’t imagine, it’s a perfect cog in HBO’s wheel of comedies.

Like “Veep,” it isn’t afraid to suggest those in authority have no clue. Like “Silicon Valley,” it hints the biggest enemy may be the one who stares back from a mirror.