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Combining various (multi-)ferroic materials into heterostructures is a promising route to enhance their inherent properties, such as the magnetoelectric coupling in BiFeO₃ thin films. We have previously reported on the up-to-tenfold increase of the magnetoelectric voltage coefficient <inline-formula> <math display="inline"> <semantics> <msub> <mi>&#945;</mi> <mi>ME</mi> </msub> </semantics> </math> </inline-formula> in BaTiO₃-BiFeO₃ multilayers relative to BiFeO₃ single layers. Unraveling the origin and mechanism of this enhanced effect is a prerequisite to designing new materials for the application of magnetoelectric devices. By careful variations in the multilayer design we now present an evaluation of the influences of the BaTiO₃-BiFeO₃ thickness ratio, oxygen pressure during deposition, and double layer thickness. Our findings suggest an interface driven effect at the core of the magnetoelectric coupling effect in our multilayers superimposed on the inherent magnetoelectric coupling of BiFeO₃ thin films, which leads to a giant <inline-formula> <math display="inline"> <semantics> <msub> <mi>&#945;</mi> <mi>ME</mi> </msub> </semantics> </math> </inline-formula> coefficient of 480 <inline-formula> <math display="inline"> <semantics> <mi mathvariant="normal">V</mi></semantics></math></inline-formula><inline-formula><math display="inline"><semantics><mi mathvariant="normal">c</mi></semantics></math></inline-formula><inline-formula><math display="inline"> <semantics> <mi mathvariant="normal">m</mi> </semantics></math></inline-formula><inline-formula><math display="inline"><semantics><msup><mrow></mrow> <mrow> <mo>&#8722;</mo> <mn>1</mn> </mrow> </msup> </semantics> </math> </inline-formula> Oe<inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mrow> <mo>&#8722;</mo> <mn>1</mn> </mrow> </msup> </semantics> </math> </inline-formula> for a <inline-formula> <math display="inline"> <semantics> <mrow> <mn>16</mn> <mo>&#215;</mo> </mrow> </semantics> </math> </inline-formula>(BaTiO₃-BiFeO₃) superlattice with a <inline-formula> <math display="inline"> <semantics> <mrow> <mn>4.8</mn> </mrow> </semantics> </math> </inline-formula> nm double layer periodicity.