Chiral partner candidate bands have been found in Rh103. As a result of this observation, a special quartet of neighboring chiral candidate nuclei can be investigated for the first time. With this quartet identified, a comparison between the behavior of the nearly degenerate doublet bands belonging to the same core but to different valence quasiparticle configurations, as well as belonging to different cores but to the same valence quasiparticle configuration, becomes possible. The comparison shows that the energy separation of these doublet band structures depends mainly on the core properties and to a lesser extent on the valence quasiparticle coupling. This observation sets up new criteria for the explanations of the band doublings, restricting the possible scenarios and providing new information on the characteristics of the underlying mechanism; it is in qualitative agreement with the chiral scenario.