Offer them the following: they can get the product they chose for the regular price, or they can buy another product (either the same or another) and get a nice discount for both, but only if the second one is going to be a gift for someone. If it’s a consumable, you might want to have a permanent sticker on it saying “A gift to X from Y – brought to you by YOUR BRAND NAME” so they are more likely to gift it. If it’s not and it’s the same product (like two copies of the same book), then that is optional.
In any case, even if they don’t gift it, it will still help grow your transaction size. If they do, it will also help you spread the word about you and the product.