Street Fighter X Tekken and its PS3 twin, it turns out. According to the manual included with both versions, the game's tag team modes allow you and a local friend to sign on to the same console and fight against two other people online; your buddy presses start at the character select screen and off you go. In actuality, this functionality only exists in the PS3 version of the game.
The issue has been acknowledged by Christian Svensson at Capcom, who stated that Capcom has no plans to patch the feature in, and that its inclusion in the manual was a mistake. "The reason for this difference is because of the architecture differences between [Xbox Live] gamertags and PSN IDs. I'm not sure of the technical details, but basically it amounts to: Sony made it so you can mix and match online and offline, and Microsoft made it so you can't."
That sounded like a reasonable explanation, until we remembered that the 360 version of Mortal Kombat does that exact thing, allowing two local players to take part in tag-team battles online. If it's possible for NetherRealm Studios to include the feature in Mortal Kombat -- the MK studio's first release under the NetherRealm banner -- its exclusion from Capcom's brand-new flagship fighter seems strange at the very least.