A story within a story. A play within a play. It was already an old technique by the time Shakespeare came along in the late 1500s so, not surprisingly, he incorporated it into several of his works.

The same “play within a play” format also suited Cole Porter 3 1/2 centuries later.

The great American composer took considerable liberties with Shakespeare’s “The Taming of the Shrew,” implanting serious drama into a bawdy comedy and, in the process, making it even more comedic.

Porter’s 1949 Tony Award-winning musical, “Kiss Me, Kate,” which incorporates the basic elements of “Taming,” opens Thursday as the final production of the 2013 Summer Lyric Theatre at Tulane University season. Show times are 8 p.m. Thursday through Saturday and 2 p.m. Sunday in Dixon Hall on the Tulane campus.

Featuring such popular Broadway show tunes as “Wunderbar,” “So in Love,” “Too Darn Hot,” “Why Can’t you Behave” and, of course, the title track, “Kiss Me, Kate” not only enjoyed a thousand-plus performance run on the Great White Way, it came back for an equally successful and award-winning revival 50 years later.

It is the 1999 revival version that director Diane Lala and the cast of the Summer Lyric production will be staging this weekend.

“This version doesn’t differ too much from the original,” Lala explained. “The biggest thing for me here is that a lot of the dance arrangements are better and bigger. The ‘Too Darn Hot’ number is longer; about 10 minutes. And we’ve added ‘From This Moment On,’ so that’s a new thing also.”

The “play within the play” during “Kiss Me, Kate” comes when some of the actors in a production of “The Taming of the Shrew” have issues with each other.

The director of the Shakespearean comedy, Fred Graham (played by Colby McCurdy), is also the lead actor, Petruchio. His ex-wife Lilli Vanessi (Katie Howe) is playing the “shrew,” Katherine. Predictably, the issues that exist between them rise to the surface during the production, making the tension onstage between Petruchio and Katherine very real.

Compounding the tension (and the humor) is the onstage presence of two gangsters (Bob Edes Jr. and Alton Geno) who are owed money by Fred; they must assume roles in the production to keep Lilli from quitting the show as she is threatening to do.

Of course, as in all Shakespeare comedies, “All’s well that ends well,” in both the Shakespeare and Porter compositions.

A native New Orleanian now teaching in the University of Cincinnati’s Musical Theatre Department, Lala is no stranger to the show, having choreographed the original version of it in Cincinnati 22 years ago.

And, keeping it in the family, her husband, Bob Pavlovich, is one of the supporting cast members in “Kiss Me, Kate,” taking on the role of General Harrison Howell.