Yes, we do. It sounds like the base you are referring to is a skin base, which is polyurethane that gives the appearance of a scalp, and the hair is injected or v-looped, depending on the base. We have skin bases with varying degrees of thickness- the HD Thin Skin (the thinnest skin base we offer, however it is only available for top of head size bases, and not available in full caps), the Micro Skin (the base is polyurethane of a medium thickness), and C-Thru Skin (the thickest skin base we offer, as it is polyurethane over a layer of silk).
You can read more about these bases here: http://www.hairdirect.com/hair/systems/skin-hair-systems.aspx
Hannah | Hair Replacement Consultant | email@example.com