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Ty Burrell just scored his second Emmy for playing oblivious but lovable Phil Dunphy on “Modern Family,” but he can be seen on the bigscreen in a very different role — as a closeted gay man in the Sundance hit “The Skeleton Twins” opposite Kristen Wiig and Bill Hader.

How did the “The Skeleton Twins” come your way? 

I’m a fan of the Duplass Brothers, who were producing, so I accepted; I guess they saw my inner repression. Actually, I loved the script, and I loved that Bill and Kristen were doing something
so different. It’s not something I’ve played before, either.

After Phil Dunphy, do you worry about typecasting?

It’s hard to worry too much about that when you’ve spent the bulk of your career unemployed. I’ve had a stable job that I’ve loved for six years. I will take that in exchange for being typecast any day of the week.

You also appeared in a Muppets movie this year. Who’s a better co-star: Bill Hader or Kermit the Frog?

I didn’t really get to work a lot with Kermit, so I’m going to go with Bill Hader on this one. But it’s really hard to beat any of the Muppets. My primary co-star in “Muppets Most Wanted” was Sam the Eagle, who is a great scene partner, very dry and very funny.

“Modern Family” makes great use of guest stars; is there anyone you’d love to have on the show? 

I’m a fan of so many people. Some of my heroes would be Steve Martin, Albert Brooks, Bill Murray.

What would Bill Murray play?

Anything he wants, of course.