  We introduce heavily separable functors of the second kind and study them in
three different situations. The first of these is with restrictions and
extensions of scalars for modules over small preadditive categories. The second
is with free functors taking values in Eilenberg-Moore categories associated to
a monad or a comonad. Finally, we consider entwined modules and give if and
only if conditions for heavy separability of the second kind for functors
forgetting either the comodule action or the module action.
