Despite their low atomic number, Al films show large spin-orbit splittings when grown on W(110). Our spin- and angle-resolved photoemission experiment reveals two types of spin-orbit split states:quantum-well states with small Rashba splitting proportional to the electron wave vector in the film plane kpar(Rashba parameter 7*10-12 eVm for a 10 monolayer film) and substrate-derived interface states with large (0.5 eV) splitting. The E(kpar) dispersion of this pair of interface states changes only slightly up to 3 monolayers of Al. At higher Al coverages the quantum-well and interface states show a remarkable avoided-crossing efect in their band dispersions. This avoided-crossing efect obeys symmetry as well as spin and, therefore, leads to a strongly enhanced spin-orbit splitting of Al quantum-well states. This is shown by E(kpar) band dispersions and by spin- and angle-resolved spectra for several thicknesses up to 15 monolayers Al.