  A study of parameter sensitivity of nuclear energy density functionals,
initiated in the first part of this work \cite{NV.16}, is extended by the
inclusion of data on ground-state properties of finite nuclei in the
application of the manifold boundary approximation method (MBAM). Density
functionals used in self-consistent mean-field calculations, and nuclear
structure models based on them, are generally "sloppy" and exhibit an
exponential range of sensitivity to parameter variations. Concepts of
information geometry are used to identify the presence of effective functionals
of lower dimension in parameter space associated with parameter combinations
that can be tightly constrained by data. The MBAM is used in an iterative
procedure that systematically reduces the complexity and the dimension of
parameter space of a sloppy functional, with properties of nuclear matter and
data on finite nuclei determining not only the values of model parameters, but
also the optimal functional form of the density dependence.
