We have a Discover card with cash back that is the same account but our card numbers are different, so we can cancel one while still being able to use the other one. Unfortunately Discover is not as widely accepted out of the USA as MC/VISA.
Consequently, we looked at MC/VISA miles cards and cash back cards and decided that the cash backs were far more flexible. We have several cards due to travel. Two of them have no "international spending" fees, but also don't have cash back. We each carry one of those on our travels outside the country so that we don't have to pay extra for the privilege of spending our money in foreign lands on meals & souvenirs. Those "exchange" fees are different from the exchange rates; it's a percentage of the purchase price, and that extra fee added on to the purchase totally cancels out any cash back from the purchase..
We learned the hard way that if your pocket is picked it's a real ***** if you have the same cards in your wallets, so by carrying a Discover and one of the two other cards each, we're pretty well covered. We have an MC/VISA type cash back card that stays a the safe in the hotel or onboard the ship (depending on mode of travel) that is for emergencies (unexpected illness, flight issues, etc.). All are paid off in full monthly.
Fun fact for the younger ones among you: That Discover card was the first card I ever got under my own name and income, post divorce in 1993. Women could not get credit cards without their husband's approval when I was in college and a young wife (mid-70s). In fact, we (my ex and I) didn't even HAVE a credit card until I was about 25, and it was in his name (he was 28). It's probably silly, but that Discover card has some special meaning for me.