Kurt Russell Teases If Other Members of His Famous Family Will Appear on “Monarch: Legacy of Monsters ”(Exclusive)

Kurt shares the screen with — and plays the same character as — his son Wyatt Russell in the Apple TV+ series

Kurt Russell and his son Wyatt Russell play the same person in the Apple TV+ series Monarch: Legacy of Monsters — but don't expect the show to become even more of a family affair in future seasons.

Wyatt, 37, is Kurt and longtime partner Goldie Hawn's only child together. However, many of their other children from past relationships and other family members are actors, including Kurt's stepchildren Oliver Hudson and Kate Hudson.

While attending a Television Academy event for Monarch at the Wolf Theatre in Los Angeles on Saturday, June 8, Kurt told PEOPLE that there are currently no plans for Hawn, 78, or his stepkids to appear on future seasons of the show.

"We don't do that," the Hateful Eight star said. "That's like slumming or something, you know what I mean? We all have our own worlds and we all have our own careers and lives in those careers and I think everybody kind of keeps it that way."

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"If you get the opportunity to work together and it makes sense, it's always great," Kurt continued, mentioning his Netflix movie franchise with Hawn, The Christmas Chronicles, and projects he's done with Kate, 45, and Oliver, 47.

He said the family stays away from what he calls "tricks" to get onscreen with each other.

Monarch marks the first live-action television continuation of the Monsterverse and follows two half-siblings (played by Anna Sawai and Ren Watabe) as they track down their family’s connection to a mysterious organization called Monarch.

Related: Goldie Hawn and Kurt Russell’s ‘Dedication’ to Their 40-Year Romance Taught Kate Hudson a ‘Powerful’ Lesson (Exclusive)

Kurt shares the role of Army officer Lee Shaw with Wyatt, who plays a younger version of the man in flashbacks.

The Crypto actor told PEOPLE that he was so blown away when he saw his son's performance as Lee that he changed his own approach to the character to push himself more.

"I was no longer really watching my son, Wyatt or anything," he said. "It really hit me that this is not a father-son thing. This is the same person, and I was going to have to kind of get a hold of some things and carry them through, and it was really building on what he was doing."

When asked about working with his father on Monarch, Wyatt recently told Variety, “I’m considered a little more laid back than my dad. I’m considered lankier, I’m languid and maybe goofier. Then I had to tell myself I couldn’t rest on those instincts because that’s not what he would do.”

As for whether old Lee and young Lee will ever meet onscreen in the sci-fi series, Kurt told PEOPLE at the Monarch event, "There's a possibility of making something happen for a year and a half now" in the show's timeline.

"All of us have that in the back of our head, but it's only if it's earned and only if it works. We don't know," he added.

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Monarch: Legacy of Monsters is streaming now on Apple TV+.

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