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Released last week, the film follows the teenage sister of Sherlock Holmes, with Claflin playing eldest sibling Mycroft.
It's based on the books by Nancy Springer - of which there are six, meaning there's plenty more of Enola's story to tell.
Speaking to LADbible, Claflin said he'd very much be up for a second installment.
"It's not in my hands, but I'd definitely be open to another one," he said.
"I had a lot of fun doing it. There's material there - and I'm always wanting more work, so my door is always open."
Claflin also admitted he felt slightly humbled to be working with such sci-fi greats as Brown and Henry Cavill - who plays Sherlock Holmes - and was delighted to share screen time with The Witcher's Geralt/Superman and Stranger Things' Eleven.
"I did feel slightly inferior, I'm not going to lie," he said. "There were no magic powers coming from my side. Someone said, 'but you were Finnick [in The Hunger Games]!' But Finnick died! He got his head ripped off by lizards. It's not a patch on those two.
"With Henry, I was mostly getting nutrition tips so I can look like him. Although I do love my beer too much to get in that sort of shape.
"It's a classic tale told in a way that feels really relevant. I loved the breaking the fourth wall element of it, it has a really fresh feel to it. Mycroft is the de facto Dad of the family really. Quite strict, trying to keep them in line.
"He doesn't like change. But I understand the competitive nature of siblings. I have younger and older brothers, me and Henry are both from big families, and you have those rivalries.
"Me and my brothers are all different but we're competitive. One invited me to a park run. I'd done no training, and he'd been training for two years. I just couldn't bring myself to lose to him though. I spent the whole last lap vomiting into my own mouth."
You can watch Enola Holmes on Netflix now.