Sabrina Caluori, the organisation's svp/digital media and marketing, discussed this subject at Advertising Age's Digital Conference 2015.
And she cited efforts including HBO Connect - initially an online platform based around real-time social TV but now shifting towards providing exclusive experiences - as well as a Viewer's Guide for Game of Thrones.
Drawing on its various experiments to date, Caluori reported that "asynchronous" extra content had proved more popular than material to be viewed while shows are on air.
It also tapped research findings which pointed to a fundamental truth about HBO. "We are called 'Home Box Office' for a reason: we deliver cinematic-like experiences," Caluori said. (For more, including detailed examples, read Warc's exclusive report: HBO learns from failure.)
"When you are in the movie theatre, you don't use your phone. You are actually paying attention to the first screen. So why are we trying to distract you on the second screen?"
Just as when watching an engrossing film, fans of HBO's shows - the network learned - were loathed to take their eyes off the primary screen, meaning they generally did not engage with its second-screen content.
"That was a key moment for us where we realised: 'It's not that people didn't like what we were putting out. It's that they don't want to be distracted from the show'," said Caluori.
"If you're watching Game of Thrones and you look down, you might miss your favourite character from the show getting killed.
"This really made us rethink the way we were thinking about second screen and social TV. Really, for us, it was this moment where we felt, 'We lost sight of our true north, of what it means for us as a brand'."
Data sourced from Warc