In the script for Ronán Noone’s one-man, one-act play “The Smuggler: A Thriller in Rhyme,” the playwright prefaces the action with several paragraphs of notes, most of them devoted to fleshing out its leading character, Tim Finnegan. Notably, “ringmaster” is the first word used to describe the Irish immigrant living in Massachusetts. “He likes to entertain,” Mr. Noone explains.

The actor playing Tim, in fact, is called on to channel 10 other characters — male and female, with varying backgrounds and accents — while shifting between three distinct rhythms: one for the “action sections” that propel the plot, another for the “expository sections,” and yet another for the “social commentary sections.” All of this must be done, as the title indicates, while speaking in verse and interacting with the audience.

In director Conor Bagley’s production, now at Irish Repertory Theatre, this means serving drinks, and doing tricks with the bottles and glasses. Scenic designer Ann Beyersdorfer has fashioned a cozy little pub, replete with chalk boards listing specials and an American flag, where Tim holds court. Our protagonist, an unproductive writer — booze and weed have proved to be lame muses — has to support himself and his wife and young son tending bar, we learn. Or he did, until the bar shut down.

Left with no source of income, Tim — played here by the beefy, commanding stage veteran Michael Mellamphy, an Irish Rep stalwart — lands a job working alongside less fortunate immigrants, men and women pirated in from south of the border to serve the overlords of an underworld festering in his mostly wealthy community.

Forced to more thoroughly ponder his own immigrant status, Tim finds himself at once frustrated and empowered, and as a result is lured into exploitative and, eventually, criminal behavior. “I look in the mirror and wonder who that is looking back at me,” he muses at one point, “and realize it is everyman doing whatever he can to maintain his family.”

Mr. Mellamphy sustains this sense of urgency, and capably manages the balance of affability and darkness his role demands. Yet it must be said that the text is not always his friend. Mr. Noone’s rhymes can strain to the point where you wish he just hadn’t bothered: “Ineffability” is coupled with “anatomy,” “off-kilter” with “silver,” and, my personal favorite, “Tina” with “mean to ya.”

There’s a sense at times that the playwright is as desperate as Tim to pique the audience. Weighing the moral implications of his actions, Tim observes that “a vagina is like a slot machine. Depending on where it drops you out it determines your destiny.” Maybe, but frankly I’m still recovering from that metaphor.

If such philosophizing can grow tiresome, it’s fun to watch as Mr. Mellamphy fields the motley crew of characters Tim summons, morphing from Tim’s dunderheaded bartender buddy to his reproachful, American-born wife to the shady, coffee-sipping Brazilian who becomes his boss. It’s an exhausting task, and Mr. Bagley lets us see the actor sweat — literally, as his Tim closes in on individual audience members, endlessly seeking affirmation.

“I’m an Amerikan,” Tim reminds us repeatedly, stressing the last syllable, which is spelled that way in the script. This is perhaps to acknowledge that others still don’t entirely accept the character as such, green card notwithstanding. They include Tim’s own rather buffoonish in-laws, who are also represented here.

Mr. Noone’s intent, clearly, is to reinforce empathy with outsiders while inviting us to ask what it truly means, right now, to be an American. Both are worthy goals, and “The Smuggler,” despite its flaws, succeeds on these basic terms and, in generally leaving us entertained, on Tim’s as well.