  We investigate the role of electronic-vibrational coupling in resonant
electron transport through single-molecule junctions, taking into account that
the corresponding coupling strengths may depend on the charge and excitation
state of the molecular bridge. In the presence of multiple electronic states,
this requires to extend the commonly used model and include vibrationally
dependent electron-electron interaction. We use Born-Markov master equation
methods and consider selected models to exemplify the effect of the additional
interaction on the transport characteristics of a single-molecule junction. In
particular, we show that it has a significant influence on local cooling and
heating mechanisms, may result in negative differential resistance, and cause
pronounced asymmetries in the conductance map of a single-molecule junction.
