The First was Facebook’s (FB) first phone with Facebook Home, customized software that modifies areas of Google’s (GOOG) popular Android operating system so users can readily check status updates and text friends. The phone is also one of Facebook’s biggest stabs at mobile yet. But stateside First sales were reportedly “a disaster,” prompting HTC to ax the smartphone’s U.K. release. Then AT&T (T), the phone’s exclusive carrier, slashed pricing to $0.99 and has reportedly decided to discontinue sales.

Now comes speculation that Facebook CEO Mark Zuckerberg approached Samsung Mobile co-CEO Shin Jong-kyun about making the next Facebook Home smartphone during a recent trip to Korea. “Facebook has every intention of becoming the second Google, and with that intent in mind, Zuckerberg is said to have asked Samsung to step up cooperation by launching a phone with a Facebook interface,” a source told The Korea Herald. 

Such stories should be taken with a grain of salt. But a Samsung smartphone with Facebook Home might not be a bad idea for either party. Sales of Samsung’s bestselling flagship Galaxy S4 smartphone have apparently slowed, causing some analysts to worry. “Samsung has yet to prove its ‘creative’ innovation, that is, launching a product or a market segment that has not existed before in addition to prowess in manufacturing technology,” the ratings agency Fitch Ratings recently told Reuters. Facebook Home may be one way for Samsung to diversify its lineup. (Extensions of the S4 line are already in the works.) In turn, Facebook could benefit from Samsung’s vast market reach — it accounted for nearly 31% of global smartphone sales during the first quarter of 2013, according to Gartner Research.

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Here are three ways Samsung could trump HTC’s effort:

Make a worthy device.  The HTC First wouldn’t have been a cutting-edge phone late last year, let alone this year. Case in point: Facebook didn’t even bother with hardware specifications during the April announcement, and now we know why. That 1.4 GHz dual-core processor, 1-gigabyte of RAM, and 4.3-inch display are ho-hum next to the Samsung S4, with its bright 5-inch full high-definition display and 1.9 GHz quad-core processor. (And let’s not even touch the more gnarly 1.6 GHz eight-core international edition.) Obviously, stylish looks and advanced parts don’t guarantee success in a market already inundated with Android smartphones, but they could help a Facebook Home phone stand out more.

Make it multi-carrier.  The HTC First’s other achilles heel was its AT&T exclusivity. AT&T remains one of the top two U.S. mobile networks, but carrier availability is obviously key to growing a healthy user base. For now at least, it’s clear very few Facebook users are willing to switch phones and carriers. So why not bring the phone to them? Having the device offered by Verizon (VZ) and even T-Mobile (TMUS) would go a long way toward upping Facebook Home’s chances at taking off.

Make more than one.  Unless it’s a new iPhone, one device does not guarantee success. Samsung, which soared on the sheer, plastic backs of many, 
many
different smartphone models, could release multiple Facebook Home devices at different price points, with different screen sizes and hardware specifications, no sweat. After all, different folks prefer different screen sizes, though smartphone customers are generally trending larger now. There could be a go-to “flagship” device and a “phablet” version with a 5-plus inch screen, to start. Our point being, the more Samsung-made devices pre-loaded Facebook Home, the better.