I've not actually tried it but I'm sure that Benefit (you can find it in Harvey Nichols or online) does something like that. I use a lot of thier other products and they are really good.
l use the I.D baremineral range of makeup, and find the face makeup is a great base. I also use the face makeup in a darker colour for an eyeshadow, and it stays put all day and night. But it a Sephora. Also Shu Umuera peach 42 is great.
it is not a base per se but i use a smidgen of elizabeth arden's eight hour balm as the tacky, petroleum jelly-like surfaces makes colour stick all day. use a TEENY amount tho!
Urban Decay's Primer Potion!! It has kept my eyeshadow perfect all day and all night if I go out. It's amazing & lasts forever. The best I've ever used, without a doubt!
I usually use my foundation as a base. You can dab as much as you want with your finger all over your eyelid or just where you need it. You can use a brush to apply it if your prefer. I have a lot of eye bases and they all work pretty good. But some people dont like to buy a lot of things so a cheap way is to just use your foundation. Its affordable and it works. So you don't have to buy a lot.