<p>We investigate the dependence of magnetoresistance (MR) on the reduced Cu thickness in infinite Co/Cu multilayers using a spin-conserving theoretical model. Electron transport is spin-dependent in Co layers and spin-independent in Cu layers. The Co/Cu interfaces are assumed to be geometrically smooth, and spin-dependent prefactors are introduced to account phenomenologically for interfacial scattering asymmetry. MR is systematically analyzed as a function of the reduced thickness d_Cu/λ_Cu​, a key dimensionless parameter governing the competition between bulk and interface scattering. For Co thicknesses (5, 30, and 50&#xa0;Å), three characteristic regimes are observed: ultrathin Co layers show a monotonic decrease of MR with increasing reduced Cu thickness due to interface-dominated scattering; intermediate Co thicknesses exhibit non-monotonic behaviour with a local maximum, revealing an optimal balance between spin-dependent transmission and current shunting; thicker Co layers display an initial slight MR increase at very small reduced Cu thicknesses, followed by a decay dominated by bulk scattering. Varying the spin-dependent prefactors modifies MR amplitudes and can induce minor non-monotonic features while preserving the overall trends. Enhancing interfacial spin asymmetry significantly amplifies MR, spanning several orders of magnitude. These results highlight the critical roles of reduced nonmagnetic-layer thickness and interfacial spin asymmetry in controlling MR, providing practical guidelines for designing high-performance Co/Cu multilayers for spintronic applications.</p>