  We deduce Diophantine arithmetic inequalities for big linear systems and with
respect to finite extensions of number fields. Our starting point is the
Parametric Subspace Theorem, for linear forms, as formulated by Evertse and
Ferretti \cite{Evertse:Ferretti:2013}. Among other features, this viewpoint
allows for a partitioning of the linear scattering, for the Diophantine
Exceptional set, that arises in the Subspace Theorem. Our perspective builds on
our work \cite{Grieve:points:bounded:degree}, combined with earlier work of
Evertse and Ferretti, \cite{Evertse:Ferretti:2013},
  Evertse and Schlickewei, \cite{Evertse:Schlickewei:2002}, and others. As an
application, we establish a novel linear scattering type result for the
Diophantine exceptional set that arises in the main Diophantine arithmetic
inequalities of Ru and Vojta \cite{Ru:Vojta:2016}. This result expands, refines
and complements our earlier works (including \cite{Grieve:2018:autissier} and
\cite{Grieve:points:bounded:degree}). A key tool to our approach is the concept
of \emph{linear section} with respect to a linear system. This was defined in
\cite{Grieve:points:bounded:degree}. Another point, which we develop in this
article, is a notion of logarithmic \emph{twisted height functions} for local
Weil functions and linear systems. As an additional observation, which is also
of an independent interest, we use the theory of Iitaka fibrations to determine
the asymptotic nature of such linear sections.
