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In order to obtain a wide-range magnetoelectric (ME) response on a ME nanocomposite that matches industry requirements, Tb0.3Dy0.7Fe1.92 (Terfenol-D)/CoFe2O4/P(VDF-TrFE) flexible films were produced by the solvent casting technique and their morphologic, piezoelectric, magnetic and magnetoelectric properties were investigated. The obtained composites revealed a high piezoelectric response (≈−18 pC·N−1) that is independent of the weight ratio between the fillers. In turn, the magnetic properties of the composites were influenced by the composite composition. It was found that the magnetization saturation values decreased with the increasing CoFe2O4 content (from 18.5 to 13.3 emu·g−1) while the magnetization and coercive field values increased (from 3.7 to 5.5 emu·g−1 and from 355.7 to 1225.2 Oe, respectively) with the increasing CoFe2O4 content. Additionally, the films showed a wide-range dual-peak ME response at room temperature with the ME coefficient increasing with the weight content of Terfenol-D, from 18.6 to 42.3 mV·cm−1·Oe−1.