Monoclinic HfO2:Eu,M (M = Li, Ta, Nb, V) powders were prepared with the Pechini method. The M-dopants were added for charge compensation of Eu3+ positioned in Hf(IV) site. This was hoped to enhance the host-to-activator energy transfer and consequently the overall efficiency of X-ray excited luminescence. Only in the case of codoping with Nb, the final phosphor did not contained any foreign phases indicating that (Eu3+,Nb(V)) pairs easily dissolved in the host. In the HfO2:Eu,V composition, the phase purity was unsatisfying for higher concentrations. However, in the case of HfO2:Eu,Ta and HfO2:Eu,Li a foreign phase/phases could be easily detected even for quite low concentrations. The addition of Ta, Nb, or V allowed to create additional absorption/excitation bands located in UV around 225–250 nm, 240–300 nm, and 240–320 nm, respectively. However, only in the presence of Nb the red Eu3+ photoluminescence could be efficiently excited and strongly enhanced upon stimulation into this extrinsic excitation structure compared to other investigated compositions as well as to singly doped HfO2:Eu reported previously. While XRDs showed that HfO2:Eu,Li contained the highest fraction of a foreign phase, this composition was found to produce the most efficient red emission upon irradiation with X-rays. It reached about 30% of the commercial Gd2O2S:Eu powder performance. This was achieved despite that a significant portion (roughly additional 30–35%) of the HfO2:Eu,Li radioluminescence was contained in a broad band covering the 400–600 nm range of wavelengths. Unfortunately, all the other codopants, Ta, Nb, and V, only suppressed the X-ray excited emission yield. Especially surprising was that the phase pure HfO2Eu,Nb powders, that presented the most efficient, truly bright photoluminescence, performed the least upon X-rays.