'The Bear' Star Abby Elliott Has a Cameo in Mind for Her Dad Chris Elliott — and He's 'Disgruntled' (Exclusive)

The Bear star Abby Elliott has a fun idea for involving her dad, Chris Elliott, in future episodes of the show.

Abby, 36, plays Carmy’s older sister Natalie, aka Sugar, on the hit FX comedy-drama. The series — which returns for season 2 on Thursday, June 22 — centers around Carmy (Jeremy Allen White), who inherits his brother Michael’s struggling restaurant following his untimely death.

Season 1 received critical acclaim with its Critics' Choice Awards and Golden Globe Awards nominations. White also earned accolades for his efforts, including a Screen Actors Guild Award.

Thinking about the show’s future, Abby tells PEOPLE exclusively who she would love to see make an appearance: her dad.

“I would love for my dad to be in it in some capacity,” she says. “That would be really, really fun.”

Her father, Chrism is an actor, comedian, director and Emmy-Award-winning writer. He first got his start in the industry by appearing in comedic sketches on Late Night With David Letterman. He starred as Chris Monsanto on Eagleheart and Roland Schitt on Schitt’s Creek. He also had recurring appearances on Everybody Loves Raymond and How I Met Your Mother. He’s known for his role in the 1993 classic comedy film Groundhog Day as well.

As for who exactly Chris would play on The Bear, Abby isn’t sure yet of the specifics. But she does have a certain character type in mind for him.

“I don’t know who he would play. Maybe a disgruntled customer,” the Saturday Night Live alum says. “Or someone in the family.”

This isn’t the first time Abby has campaigned for someone to appear in the FX series. In an interview with The Daily Beast’s The Last Laugh podcast, she revealed that she would love for actress Joan Cusack to play Sugar and Carmy’s mother, who has yet to appear on screen.

Abby explained that the idea came to her when she and Chris Witaske, who plays her husband Pete on The Bear, wandered into Cusack’s famous boutique while they were shooting the series in Chicago.

“[Cusack] is very much living in her own world,” she said on the podcast. “She does not want to be an actress, really, anymore, but I think that her playing my mother — wouldn’t that be cool?”

While her character Sugar’s family may be a little more complicated and dark, Abby has nothing but fond memories of growing up with her comedian father. In an appearance on Larry King Now in 2020, she said it was “the best” having him for a dad.

“He was always there to make us laugh,” she recalled. “He was so funny at home. He used to pick us up from school with a sign that said 'Elliott' like he was our chauffeur.”

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All episodes of The Bear seasons 1 and 2 are available to stream now on Hulu.