A vector vortex beam presents local polarization states that are spatially modulated in the plane transverse to propagation. By employing a two-crystal-sandwich source allowing for nonlinear interactions between input fields of any polarization, we analyze experimentally the process of stimulated parametric down-conversion and observe unique effects when the pump and seed fields are vector vortex beams. We reconstruct the transverse polarization pattern of the generated idler beam by Stokes polarimetry. The experimental results obtained are in good qualitative agreement with theory and exhibit manifold polarization transverse distributions for different combinations of pump and seed vector vortex beams, which may find applications in both classical and quantum optics.