We propose to probe both the CPT and CP violation together with the search for sterile neutrinos in one do-it-all experiment. This omnibus experiment would utilize neutrino oscillometry with large scintillator detectors like LENA, JUNO or RENO-50 and manmade radioactive sources similar to the ones used by the GALLEX experiment. Our calculations indicate that such an experiment is realistic and could be performed in parallel to the main research plan for JUNO, LENA, or RENO-50. Assuming as the starting point the values of the oscillation parameters indicated by the current global fit (in 3 active + 1 sterile scenario) and requiring at least 5 sigma confidence level, we estimate that with the proposed experiment we would be able to detect CPT mass anomalies of the order of 1% or larger.