  We perform a dynamical system analysis and a Bayesian model selection for a
new set of interacting scenarios in the framework of modified holographic Ricci
dark energy models (MHR-IDE). The dynamical analysis shows a modified radiation
epoch and a late-time attractor corresponding to dark energy. We use a
combination of background data such as type Ia supernovae, cosmic chronometers,
cosmic microwave background, and baryon acoustic oscillations measurements. We
find evidence against all the MHR-IDE scenarios studied with respect to
$\Lambda$CDM, when the full joint analysis is considered.
