The possibility of controlling the interfacial properties of artificial oxide heterostructures is still attracting researchers in the field of materials engineering. Here, we used surface sensitive techniques and high-resolution transmission electron microscopy to investigate the evolution of the surface spin-polarization and lattice strains across the interfaces between La_0.66Sr_0.33MnO₃ thin films and low-doped manganites as capping layers. We have been able to fine tune the interfacial spin-polarization by changing the capping layer thickness and composition. The spin-polarization was found to be the highest at a critical capping thickness that depends on the Sr doping. We explain the non-trivial magnetic profile by the combined effect of two mechanisms: On the one hand, the extra carriers supplied by the low-doped manganites that tend to compensate the overdoped interface, favouring locally a ferromagnetic double-exchange coupling. On the other hand, the evolution from a tensile-strained structure of the inner layers to a compressed structure at the surface that changes gradually the orbital occupation and hybridization of the 3d-Mn orbitals, being detrimental for the spin polarization. The finding of an intrinsic spin-polarization at the A-site cation observed in x-ray magnetic circular dichroism (XMCD) measurements also reveals the existence of a complex magnetic configuration at the interface, different from the magnetic phases observed at the inner layers.