  We investigate the response of the bound state structure of a two-boson
system, within a Yukawa model with a scalar boson exchange, to the inclusion of
the cross-ladder contribution to the ladder kernel of the Bethe-Salpeter
equation. The equation is solved by means of the Nakanishi integral
representation and light-front projection. The valence light-front wave
function and the elastic electromagnetic form factor beyond the impulse
approximation, with the inclusion of the two-body current, generated by the
cross-ladder kernel, are computed. The valence wave function and
electromagnetic form factor, considering both ladder and ladder plus
cross-ladder kernels, are studied in detail. Their asymptotic forms are found
to be quite independent of the inclusion of the cross-ladder kernel, for a
given binding energy. The asymptotic decrease of form factor agrees with the
counting rules. This analysis can be generalized to fermionic systems, with a
wide application in the study of the meson structure.
