It has recently been shown that the transmission of electromagnetic fields through subwavelength slits (parallel to the electric field direction) in a thin metallic screen can be greatly enhanced by covering one side of the screen with a metallic cut-wire array laid on a dielectric layer. In this Letter, we show that a richer phenomenology (which involves both electric- and magnetic-type resonances) can be attained by pairing a second cut-wire array at the other side of the screen. Via a full-wave comprehensive parametric study, we illustrate the underlying mechanisms and explore the additional degrees of freedom endowed, as well as their possible implications in the engineering of enhanced transmission phenomena.