In the work reported here, we have considered the interaction between modified holographic Ricci dark energy, a particular choice of Nojiri–Odintsov cut-offs, and pressureless dark matter for three different choices of scale factor, namely logamediate, intermediate, and emergent. Two different interaction terms have been considered. In one case, the interaction has been taken proportional to the dark energy density; in the other case, it has been taken proportional to the matter density. In the case of Q =3 Hδρ x , we have observed that there is a crossing of phantom boundary and the equation of state parameter has been observed to behave like quintessence. The influence of various parameters in the scale factors has also been observed. Also, an exit from phantom phase has been observed for the choice of scale factor in the emergent form. Considering the interaction term Q to be proportional to the matter density for logamediate scale factor, w x has been found to behave like quintessence, i.e. >−1. For the emergent scale factor in this interaction scenario, the model has been found to lead to a w x parameter lying in the region ≤−1. Therefore, in general, it has been found that Q =3 Hδρ x is more suitable than Q =3 Hδρ m in creating a model having a w x parameter crossing the phantom boundary.