I've done this on a number of occasions over the years with both Debit and Credit cards, splitting the cost between two of my cards or splitting it with a friend and never encountered any difficulty. Even restaurants that state "no splitting bills" because they don't want time wasted as six people pick through a long bill will often allow you to do a simple payment split (like 50/50) between two cards. It also occurs a lot with gift cards (e.g. one4all which are processed like a credit/debit card) where you go on to use your credit/debit card to pay the balance due after the funds on the gift card are fully used.
Do you accept divided payments? The majority of internet retailers won't let you divide your payment. When making a purchase, online shops may let you combine a gift card with a credit card, but they seldom permit consumers to do the same with two credit cards or a combination of a credit and debit card.
none whatsoever and more common that you think especially if the store takes gift cards.
Makes no difference to the store either
Online is different as payment gateways can't handle a split payment. A workaround online is f the store sells gift certificates that can be used before the payment is made. In that case one card buys a gift certificate and the other card does the balance payment