“Alpha House” isn’t the most popular or celebrated title amid the present onslaught of D.C.-set political series, but it might be the most honest and politically astute. Perhaps that’s because Garry Trudeau’s satire about a quartet of Republican senators sharing living quarters in Washington doesn’t pussyfoot around questions of partisanship (a la “Veep” and “Madam Secretary”) or mangle reality in pursuit of melodrama and florid flights of fancy (“Scandal,” “House of Cards”). As such, this Amazon series appears content to skewer selected targets, choose sides and let the chips fall where they may.

Appropriately returning just in time for the midterm elections, the second season finds the show loading up on star cameos from Hollywood (Bill Murray), media (Matt Lauer, Trudeau’s wife Jane Pauley, John King) and the world of political wonks (Grover Norquist, David Axelrod). Still, the formula and situations remain largely the same, with each of the solons grappling with various challenges and indignities.

In the case of good ol’ boy coach-turned-North Carolina Sen. Gil John Biggs (John Goodman), that includes unexpected election competition. Meanwhile, Florida presidential aspirant/resident sex-addict Sen. Andy Guzman (Mark Consuelos) lurches toward the altar with his latest girlfriend (Yara Martinez, pulling double duty in “Jane the Virgin”), Pennsylvania’s Sen. Robert Bettencourt (Clark Johnson) endures marital troubles, and Nevada Sen. Louis Laffer (Matt Malloy) keeps finding new ways to humiliate himself, whether that’s awkwardly addressing a gay staff member or foolishly agreeing to publicly perform standup comedy.

On top of that, Gil John’s kid has signed on to appear in a reality show titled “Real Daughters of D.C.,” even as her dad butts heads with a very-right-wing senator (Janel Moloney) who wants to establish a permanent Benghazi committee, and thinks open-carry gun laws should extend into the Capitol.

Although Trudeau obviously doesn’t harbor much sympathy for his protagonists’ policies, the satire still exhibits a modicum of empathy toward their various professional and personal struggles, such as Robert’s pained expression when a colleague (played by Wanda Sykes) roasts him for being a black Republican.

Foremost, “Alpha House” (which was loosely inspired, it bears repeating, by a real living arrangement involving lawmakers) exhibits savvy about the quirks of Washington as well as the vagaries of politics and media, while still managing to be pretty consistently funny. So the show can shift gears from insider humor like talking about using “dark money” to finance ads that savage a political rival, to silly stuff like Louis’ prized acquisition of a George W. Bush painting, which he naturally refers to as “My Bush.”

Granted, with all the praise rightfully showered on Amazon’s latest series “Transparent,” starring Jeffrey Tambor, “Alpha House” and the Silicon Valley comedy “Betas” might wind up being asterisks in the coming-of-age tale the company is writing regarding its nascent programming efforts.

Based on these previewed episodes, however, Trudeau and his team continue to deliver a show that , while perhaps not the out-and-out smartest scripted inside-the-Beltway series around, qualifies at the very least for the runoff.