We discuss the physics potential of intermediate L ∼ 20 ÷ 30 km baseline experiments at reactor facilities, assuming that the solar neutrino oscillation parameters ∆m 2 ⊙ and θ⊙ lie in the high-LMA solution region. We show that such an intermediate baseline reactor experiment can determine both ∆m 2 ⊙ and θ⊙ with a remarkably high precision. We perform also a detailed study of the sensitivity of the indicated experiment to ∆m 2 atm , which drives the dominant atmospheric νµ (νµ) oscillations, and to θ -the neutrino mixing angle limited by the data from the CHOOZ and Palo Verde experiments. We find that this experiment can improve the bounds on sin 2 θ. If the value of sin 2 θ is large enough, sin 2 θ > ∼ 0.02, the energy resolution of the detector is sufficiently good and if the statistics is relatively high, it can determine with extremely high precision the value of ∆m 2 atm . We also explore the potential of the intermediate baseline reactor neutrino experiment for determining the type of the neutrino mass spectrum, which can be with normal or inverted hierarchy. We show that the conditions under which the type of neutrino mass hierarchy can be determined are quite challenging, but are within the reach of the experiment under discussion.