  This paper uses convex integration with avoidance and transversality
arguments to prove the relative $h$-principle for closed
$\mathrm{SL}(3;\mathbb{R})^2$ 3-forms on oriented 6-manifolds. As corollaries,
it is proven that if an oriented 6-manifold $\mathrm{M}$ admits any
$\mathrm{SL}(3;\mathbb{R})^2$ 3-form, then every degree 3 cohomology class on
$\mathrm{M}$ can be represented by an $\mathrm{SL}(3;\mathbb{R})^2$ 3-form and,
moreover, that the corresponding Hitchin functional on
$\mathrm{SL}(3;\mathbb{R})^2$ 3-forms representing this class is necessarily
unbounded above. Essential to the proof of the $h$-principle is a careful
analysis of the rank 3 distributions induced by an
$\mathrm{SL}(3;\mathbb{R})^2$ 3-form and their interaction with generic pairs
of hyperplanes. The proof also introduces a new property of sets in affine
space, termed macilence, as a method of verifying ampleness.
