Here in the US, Discover Card offers this as one of their card benefits, but only certain stores participate. It's called Discover Cash Over. Basically, at a participating store, when you purchase using a Discover Card, you'll have the option to also get some cash back (say, $20 or $40). There's a daily limit that Discover sets, and individual stores can also set their own more restrictive limits.
It doesn't count as a cash advance (so no special interest rate, and the interest has the same grace period as a regular purchase). So say you bought some shoes for $50, and did $20 cash over. The statement would show ($50 + $20) for that transaction. I'm not aware of another card that offers this service, but keep in mind it still can't be used to increase your rewards since Discover would only calculate your rewards for the actual purchase price, not the cash over.
One reason that this isn't very common is that merchants pay a percentage of the purchase price to the card network. Asking for $100 cash on top of the purchase price means the merchant would be paying a much more disproportionate transaction fee in relation to the actual price of the goods sold. For this reason, even if they did allow it, they would have to be getting the money somehow (such as higher priced goods).
I am guessing Discover handles these in a way that doesn't charge the merchant extra transaction fees for the cash over portion.