Many shooters of this era require online connection for you to experience their games communities. It saddens me to say that I believe Destiny will not be able to support split screen on the hardware it's working with, at least on current generation. Bungie has already stated that they are pushing current generation consoles to the limit. But, should you be able to play online, you will never be alone, in the most comforting way you can imagine someone saying that.
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Maybe split screen for xbox one and ps4 then? Or at least just 2 player local.