"If I had to guest star in anything, it'd be The Fall," she told us. "I'd love to play a villain. The writing on that show is fantastic and it really holds your attention."
While we'd love to see Piper, sorry Schilling, give Jamie Dornan's Paul Spector a run for his money, the actress probably has enough to be getting on with right now. As well as her ongoing role in OITNB, she currently stars in new comedy film The Overnight, alongside Jason Schwartzman and Adam Scott.
Schilling plays one half of a couple who move to LA and end up having dinner with another couple who want them to take part in some group sexual antics. The opening scene, in which Schilling's character and her husband have the kind of sex that only comes in long term relationships, will make even the most surly of viewers laugh. It's a definite departure from her role as Piper.
"I wasn't specifically looking for someone different to Piper, but it's a thrill it ended up that way, even though that wasn't my intention," she said. "I'm not used to the comedy world, so everyone's ability to keep a straight face in certain scenes was amazing to me. I do a good job of that part."
Although comedy is a new arena for Schilling, there are elements of the film that follow the same OITNB themes of self-acceptance and discovery - something that she is still seeking out in herself.
"I struggle with anxiety and fear," she said. "Both of those things can be hard. Career success has helped, but these things are internal - the external doesn't fix everything."
While The Overnight is packed full of laughs, it's also a tender look at relationships and how the successful kind develop.
"You can love someone, but some things are difficult and need to be addressed," she said. "Deciding to expose the truth feels frightening, but that's how things grow. As you grow as an individual, so will your relationship."
Schilling's ascent to stardom feels sudden, but she's been working in acting since 2007 when she played a supporting role in independent film Dark Matter. This led to a part as a nurse in NBC TV show Mercy, before she landed a role opposite Zac Efron in The Lucky One. In 2013, she auditioned for Netflix TV show OITNB and bagged the lead of Piper, a middle class young woman who ends up in prison for a crime that happened in her long ago past. She's a divisive character - naive and well-intentioned, but also self-absorbed and manipulative. Does Schilling herself like Piper?
"She's trying," she says. "She's not stuck in her ways and she's really looking for a way to be... She's looking for some truths. I can relate to her; that feeling of how in these circumstances can I adjust; how can I bring more parts of myself to the table. That's what Piper's doing."
Season three of the show has seen a new addition to the show - Ruby Rose, a new love interest of Piper, and a character who has attracted much attention for being everyone's new girl crush.
"Do I fancy Ruby? Why would anyone not like her?" says Schilling. "She's wonderful. The character is spot on and she's really shaken up the dynamic. She's a brilliant addition."
There seems to be no end in sight yet for OITNB (thankfully), but Schilling has a clear idea about how she wants things to pan out for her character.
"I'd like her to find a way to live that embraces all the things that she is and that she's becoming," she said. "She has such a small identity when she first went to prison and I'd like her to have a bigger sense of herself and self-acceptance. Romantically, I hope that whoever she ends up with aids that process for her."
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