I’ve seen from the trophy list for the game that there are some DLC packs for Doom 2016 on the PS4. Are any of these DLC packs for the single player story mode or are they multiplayer only?
No, All of the DLC released for Doom is for the multiplayer component of the game. There are no story based DLC packs for the game and it doesn’t look like they had any plans to. Maybe they will release a mini game sort of like a stand alone DLC in the future, but as of right now all of the DLC has been released and is free of charge in update 6.66