The linear polarization of x-rays, emitted from highly-charged ions, has been studied within the framework of the density matrix theory and the multiconfiguration Dirac-Fock method. Emphasis was placed especially on two-photon cascades that proceed via intermediate overlapping resonances. For such two-step cascades, we here explore how the level-splitting of the resonances affects the linear polarization of the x-rays, and whether modifications in the degree of polarization may help determine small level-splittings in multiply- and highly-charged ions, if carefully analyzed along isoelectronic sequences. Detailed calculations are carried out for the 1s2p² Jᵢ = 3/2 → 1s2s2p J = 1/2, 3/2 + γ1 → 1s²2s Jf = 1/2 + γ₁ + γ₂ radiative cascade of lithium-like W⁷¹⁺ ions. For this cascade, a quite remarkable increase of the (degree of) linear polarization is found for the second-step γ2 photons, if the level-splitting becomes smaller than Δω ≲ 0.2 a.u. ≈ 5.4 eV. Accurate polarization measurements of x-rays may therefore be also utilized in the future to ascertain small level-splittings in multiply- and highly-charged ions.