Canopy Co. in late 2012 hoped to drive a change in the way people interact with their iPhones, but it wasn’t prepared when Apple Inc. redesigned the product that fall.

After spending last year back at the drawing board, executives from the Minneapolis company last week unveiled their latest concept for a pressure-sensitive case that wraps around the iPhone, essentially extending the phone’s touch-screen interface to its entire surface.

The product, called Sensus, is a moonshot idea for the 13-employee company that’s been backed by nearly $4 million in venture capital.

Success depends on Canopy’s ­ability not just to interest retailers and consumers but also software developers, who would need to rewrite programs to take advantage of the case’s ability to allow new inputs of the iPhone.

“We want to make sure that upon the release of the Sensus we have a value proposition,” Andrew Kamin-Lyndgaard, Canopy’s chief executive, said in an interview. “So we want to make sure there is a wide range of applications, not only games that are likely to garner a lot of attention, but utility, productivity and photography apps, and apps to make the iPhone accessible for people who are sight-challenged or completely blind.”

He and other executives spent last week at the Consumer Electronics Show drumming up retailer and media interest in the device.

And they’ve sent versions of the case to about 1,000 software developers in hopes they will adapt new or existing apps to work with Sensus, which they hope to put on the market in the first half of the year.

“Whether they’ll attract developers is yet to be seen,” said Jake Joraanstad, who tracks iPhone-related accessories for his app-writing firm, Myriad Mobile of Fargo, N.D. “But I think Canopy is getting in at the right time because Apple is making a huge push for gaming right now and nobody else is doing what Canopy’s doing.”

The Sensus iPhone case should appeal to game ­players because game controls would no longer be confined to the iPhone’s relatively small screen, Joraanstad said. Instead, a game could be controlled by tapping fingers on the sides and back of the case.

Barbara Stinnett, Canopy’s executive chairman, said the company has signed up one electronics distributor, whom she declined to name, and is looking for two more. Where the product will be manufactured depends on where the distributors are based, she said.

Based on advice from prospective retailers, Canopy is considering a retail price of about $99 for Sensus, the high end of the price range the firm had contemplated for the first version of its product a year ago.

The original Sensus case, which executives unveiled at last year’s CES, had pressure switches only on the edges. The company didn’t bring the product to market, however, because it was designed to connect to the 30-pin electronic connector on the bottom of versions of the iPhone before the iPhone 5, which debuted in late 2012 with an 8-pin connector.

Canopy executives decided they couldn’t risk introducing a product that only worked with older iPhones.

“Retailers only want to put forward products that are the latest and greatest devices,” Kamin-Lyndgaard said. “And we have only one opportunity to do it right.”

Canopy redesigned the case for the iPhone 5 and 5s models. They changed the touch-sensitive sensors that were similar to those on the iPhone screen for pressure-sensitive sensors that send a different signal to the phone depending on whether they were lightly or firmly touched.

New iPhone apps designed to work with the case “will be controlled not by touch alone, but by the degree of touch,” Kamin-Lyndgaard said. “That would allow the developer of a driving game to control the accelerator and brake through finger pressure on the side of the case instead of swiping a finger up or down on the screen. In a photo application, you could use finger pressure to hold the ‘shutter button’ only halfway down to lock in exposure or color balance.”

With the product revamp and market delay, Canopy added three employees last year. But further growth depends on bringing the product to market and raising more capital.

“We don’t need to add more people for the Sensus launch,” Stinnett said. “But when we get more funds we’ll look to add depth and breadth to the company.”