  We prove that given a finite rank free group $\mathbb{F}$ of rank $\geq 3$
and two exponentially growing outer automorphisms $\psi$ and $\phi$ with dual
lamination pairs $\Lambda^\pm_\psi$ and $\Lambda^\pm_\phi$ associated to them,
and given a free factor system $\mathcal{F}$ with co-edge number $\geq 2$,
$\phi, \psi $ each preserving $\mathcal{F}$, so that the pair $(\phi,
\Lambda^\pm_\phi), (\psi, \Lambda^\pm_\psi)$ is independent relative to
$\mathcal{F}$, then there $\exists$ $M\geq 1$, such that for any integer $m,n
\geq M$, the group $\langle \phi^m, \psi^n \rangle$ is a free group of rank 2,
all of whose non-trivial elements except perhaps the powers of $\phi, \psi$ and
their conjugates, are fully irreducible relative to $\mathcal{F}$ with a
lamination pair which fills relative to $\mathcal{F}$.
  In addition if both $\Lambda^\pm_\phi, \Lambda^\pm_\psi$ are non-geometric
then this lamination pair is also non-geometric.
  We also prove that the extension groups induced by such subgroups will be
relatively hyperbolic under some natural conditions.
