The Glimmerglass Opera has four productions on its bill this summer, and each employs a shared backdrop: an elegant facsimile of an Elizabethan theater in pale gray timber. In front of that background, the flats and scenery for each opera float in. Operagoers who attend performances to applaud lavish sets rather than the singing and staging may be disappointed by it, but the ingenious device — which is both artistically apt and economical — successfully unifies the quartet under a single theme: operas based upon stories that inspired Shakespeare.

In Vincenzo Bellini’s “I Capuleti e i Montecchi,” Shakespeare’s world of rival families is set in a sinister city-state where Giulietta’s vicious family, the Capuleti, are firmly in the ascendant. Romeo’s murderous Montecchi tribe is resisting defeat despite being firmly cast out. Anne Bogart’s robust, masculine production has opposing choruses draped in black leather trench coats and brandishing staves; this is not Franco Zeffirelli’s peachy Verona, nor Baz Luhrmann’s Verona Beach. Her production brings to the fore the turmoil in the Capulet household as simmering vengeance for a lost son, struck dead by Romeo in battle. The rage comes to fog the mind of the patriarch (Christopher Job) as he insists upon marrying Giulietta (Sarah Coburn) to Tebaldo (John Tessier). Romeo (Emily Righter) smuggles himself into the city palace in disguise to pursue Giulietta, his priapic passion made even more ardent because it is forbidden.

In one of those real-life dramas that heighten live performance, Ms. Righter was a last-minute switch for the indisposed Sandra Piques Eddy, and by golly did she grasp her chance with both larynxes. Her Romeo was dashing, brave, boyish, sexy, and brilliant of voice, an ample vindication of Glimmerglass’s Young American Artists Program, from which she sprang. Combined with Ms. Coburn’s affecting and wistful Giulietta, the adolescent tryst seemed authentic, setting innocent infatuation against realpolitik, love against hate.

Handel’s “Giulio Cesare in Egitto” — which, in fact, is more the Bard’s “Cleopatra” than his “Julius Caesar” — is relocated by director Robin Guarino to Benito Mussolini’s time, with a battle map suggesting the 1936 Ethiopian adventure for those who don’t get the fascist reference the first time. Il Duce’s absurd ambition to revive a new Roman Empire is hardly a neat fit, but the conceit adds a jaunty strut in the step of Laura Vlasak Nolen’s confident and beautifully wrought Cesare, who meets his match in Lyubov Petrova’s sizzling Cleopatra.

In evidence is more than a little of the absurdity of “Scoop,” Evelyn Waugh’s comic novel about reporting Italy’s farcical attempt to belatedly gain an African foothold, as a fez-donning Tolomeo, a dead ringer for King Farouk, is skillfully played for laughs and pathos by Gerald Thompson. With beheadings, shootings (there is a lot of gun action this year at Glimmerglass), seductions, and dream sequences, the more than three hours fly by.

Of the four productions, I expected the odd one out to be Cole Porter’s “Kiss Me, Kate,” the first Broadway musical to be presented by the company. But in the end, it was “Das Liebesverbot,” or “The Forbidden Love,” a piece of Wagnerian juvenilia — he wrote both music and libretto when he was 21 — based upon “Measure for Measure.” Wagner was under the influence of Bellini at the time, though the Sicilian’s lightness of touch mostly eluded him.

The production would have been an interesting collectors’ item were it not for Nicholas Muni’s capricious decision to abandon the opera’s central moral dilemma: the surprise hypocrisy of the moralist gauleiter Friedrich (Mark Schnaible), whose equilibrium is fatally upset by the innocent sensuality of the ethereal novice Isabella (Claudia Waite) when she kneels to plead for the life of her brother Claudio (Richard Cox), who has made Mariana (Holli Harrison) pregnant out of wedlock.

Drawing a little on German Expressionism and far too much on John Waters’s “Pink Flamingos,” Mr. Muni recasts Isabella as a cigarette-smoking, lipstick-donning, handbag-swinging, cross-dressing vamp, forcing viewers to consider how Mr. Waters’s muse Divine might have handled the part. Instead of inadvertently arousing Friedrich with her virginal piety, Mr. Muni’s nun hauls him in like a dock tart in fishnets welcoming sailors on shore leave.

So, on to “Kiss Me, Kate,” which proves that the right musical is every bit as appropriate a Glimmerglass leavener as the operettas proffered in the past. After the revival of “South Pacific” at Lincoln Center, who can now doubt that there is as much intellectual worth in reviving an intelligent piece of musical theater as, say, a middling piece of Gilbert and Sullivan?

Diane Paulus’s “Kate” moves along at a hectic comic pace, with Lisa Vroman’s Lilli/Kate spiritedly played as a man-hating closet dominatrix scorned by her double-dealing ex-husband Fred/Petruchio, a well-turned if rather too stolid Brad Little. The staging is unexpected and ingenious. The sets, fresh and exciting; the chorus direction inventive and involving. If some of the voices are not quite what we might expect from an opera company venturing onto the Great White Way, the gusto more than makes up. And the hilarious handling of the hood duet “Brush Up Your Shakespeare” by Michael Mott and Brad Nacht, tenors posing as Sopranos, stops the show in its tracks. Broadway producers in search of a ready-made production for an empty theater this fall should head to Cooperstown without delay.

Until August 24, 7300 State Highway 80, Cooperstown, N.Y. 607-547-2255.