We discuss the effects of the brane-localized mass terms on the fixed points of the toroidal orbifold T2/Z2 under the presence of background magnetic fluxes, where multiple lowest and higher-level Kaluza-Klein (KK) modes are realized before introducing the localized masses in general. Using linear algebra, we find that, in each KK level, one or more of the degenerate KK modes are almost inevitably perturbed, when single or multiple brane-localized mass terms are introduced. When the typical scale of the compactification is far above the electroweak scale or the TeV scale, we apply this mechanism for uplifting unwanted massless or light modes which are prone to appear in models on magnetized orbifolds. © 2017 American Physical Society.