You can rebind a Dualshock 4's buttons to a long list of alternative actions in the game and the game's default control scheme already supports more functions than the pad has buttons, through button combinations, so surely having extra buttons available wouldn't be a problem...

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(Even only using the DS4's four face buttons, four shoulder buttons and four director buttons, that gives you 479,001,600 possible factorial button combinations and adding the pads' L3 and L4 buttons gives you 87,178,291,200 combinations, not that anyone could every remember all the pads possible combinations, have the dexterity or available fingers to press all the pads' buttons at once or that any developer could possibly programme all those possible functions into a game, but still, no modern game system is realistically limited by its' default control devices' physical buttons...

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Also, while i've never bought a third party pad for any of my Playstations, the PS1, 2 and 3 all support third party, generally unlicenced, pads and i'd say the PS4 does as well...

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