  We extend results about $n$-shifted coisotropic structures from part I of
this work to the setting of derived Artin stacks. We show that an intersection
of coisotropic morphisms carries a Poisson structure of shift one less. We also
compare non-degenerate shifted coisotropic structures and shifted Lagrangian
structures and show that there is a natural equivalence between the two spaces
in agreement with the classical result. Finally, we define quantizations of
$n$-shifted coisotropic structures and show that they exist for $n>1$.
