  We study meson-meson interactions using an extended $q^2\bar{q}^2(g)$ basis
that allows calculating coupling of an ordinary meson-meson system to a
hybrid-hybrid one. We use a potential model matrix in this extended basis which
at quark level is known to provide a good fit to numerical simulations of a
$q^2\bar{q}^2$ system in pure gluonic theory for static quarks in a selection
of geometries. We use a combination of resonating group method formalism and
Born approximation to include the quark motion using wave functions of a
$q\bar{q}$ potential within a cluster. This potential is taken to be quadratic
for ground states and has an additional smeared $\frac{1}{r}$ (Gaussian) for
the matrix elements between hybrid mesons. For the parameters of this
potential, we use values chosen to 1) minimize the error resulting from our use
of a quadratic potential and 2) best fit the lattice data for differences of
$\Sigma_{g}$ and $\Pi_{u}$ configurations of the gluonic field between a quark
and an antiquark. At the quark (static) level, including the gluonic
excitations was noted to partially replace the need for introducing many-body
terms in a multi-quark potential. We study how successful such a replacement is
at the (dynamical) hadronic level of relevance to actual hard experiments. Thus
we study effects of both gluonic excitations and many-body terms on mesonic
transition amplitudes and the energy shifts resulting from the second order
perturbation theory (i.e. from the respective hadron loops). The study suggests
introducing both energy and orbital excitations in wave functions of scalar
mesons that are modelled as meson-meson molecules or are supposed to have a
meson-meson component in their wave functions.
