Generally (though not always) the drivers in open headphones are engineered in such a way that covering them removes a lot of the sound.
I don't know if this is the case for the DT880s, but I do know that my Grados suffer greatly if I cover the open grilles.
Listen to some music with them and cover the grille on the back with your hands. Does it change the sound? My guess is probably, but I'm not sure.
I would say that if your budget allows, add some closed headphones...