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In this work, elastic properties of Mg-based bulk metallic glasses (BMGs) with different chemical compositions were investigated. By compositional tuning in the quaternary Mg-Cu-Ag-Y alloys, the Poisson's ratio nu of 0.332 is achieved at Mg(56)Cu(21)Ag(14)Y(9) BMG, in excess of the previously suggested critical value (nu = 0.31-0.32) for the brittle-to-tough transition in metallic glasses. With the properties of the constituent elements, the predicted values of the bulk modulus B and shear modulus mu of Mg-based BMGs are 8% and 10% greater than the measured value, respectively. Notch toughness K(Q) of the ten investigated Mg-based BMGs varies between 3.6 and 8.2 MPa root m. Intrinsic brittleness of Mg glass is associated with its tiny plastic zone size (in micrometer scale) and weak resistance to crack propagation. The toughness variations are lack of significant correlation with the m or l. Among the investigated alloys, the Mg(59.5)Cu(22.9)Ag(6.6)Gd(11) BMG manifests a good combination of improved toughness and high glass-forming ability.