  We report the observation of above-threshold dissociation of a multielectron
molecular system, Na$_2^+$. The process is due to continuum-continuum
transitions in a field-dressed molecular continuum. Three well resolved
fragmentation channels with different kinetic energy release patterns have been
detected, of which, two are associated with ordinary photodissociation via
light-induced potentials into Na(3s) + Na$^+$ and Na(3p) + Na$^+$, and one with
continuum-continuum transitions and above-threshold dissociation into Na(3p) +
Na$^+$. We show that when we dress this molecule with a field whose intensity
is ~3 x 10$^{12}$ W/cm$^2$, above-threshold dissociation prevails over other
processes, such as field-ionization followed by Coulomb explosion.
