  We examine a spatially flat Friedmann-Robertson-Walker (FRW) universe filled
with interacting dark matter and a modified holographic Ricci dark energy
(MHRDE). The interaction term is selected as a significant rational function of
the total energy density and its first derivative homogeneous of degree. We
show that the effective one-fluid obeys the equation of state of a relaxed
Chaplygin gas, then the universe turns to be dominated by pressureless dark
matter at early times and undergoes an accelerated expansion in the far future
driven by a strong negative pressure. Performing a $\chi^{2}$-statistical
analysis with the observational Hubble data and the Union2 compilation of SNe
Ia, we place some constraints on cosmological parameters analyzing the
feasibleness of the modified holographic Ricci ansatz. It turned that MHRDE
gets the accelerated expansion faster than the $\Lambda$CDM model. Finally, a
new model with a component that does not exchange energy with the interacting
dark sector is presented for studying bounds on the dark energy at early times.
