No, Days Gone is simply a single player. Unfortunately, if you are hosting a Days Gone party at your house, you will need to have separate Play Station 4s in order for others to be playing the game at the same time as the others. At your party, each person would need to play Days Gone individually and separately. Each would have to take a turn because Days Gone does not have multiplayer.
However, the fun is not lost. You can still have a great Days Gone party by either having your friends and partygoers to bring their own Play Station 4. With all of your television sets, hook each play station 4 to the TV and let your friends go wild playing on their own set.