  Given a class of embeddings into a contact or a symplectic manifold, we give
a sufficient condition, that we call isocontact or isosymplectic realization,
for this class to satisfy a general $h$-principle. The flexibility follows from
the $h$-principles for isocontact and isosymplectic embeddings, it provides a
framework for classical results, and we give two new applications. Our main
result is that embeddings transverse to a contact structure satisfy a full
$h$-principle in two cases: if the complement of the embedding is overtwisted,
or when the intersection of the image of the formal derivative with the contact
structure is strictly contained in a proper symplectic subbundle. We illustrate
the general framework on symplectic manifolds by studying the universality of
Hamiltonian dynamics on regular level sets via a class of embeddings.
