Are there programs that issue Mastercards instead of Visa or AmEx?

All I have is a bunch of VISA cards and a couple of American Express.

I have a local store that will only accept Mastercard so I don't earn any points when I use cash/check.

Bank of America, Barclay's, Chase, and Citibank are all MasterCard issuers.

Many Citicard applications allow the customer to choose which version to receive.

By default, Chase personal cards are issued as VISA, but you can obtain a MasterCard version if you start the application process here:

http://www.mastercard.us/personal-select.html

By default, Chase Ink (small business) cards are issued as MasterCard.

That's not a complete list, though. If I go there and select Rewards Cards, it never lists the Amtrak Guest Rewards card from Chase, which is MC by default:

https://creditcards.chase.com/lp/amtrak/AGR/?CELL=655P

And so if that one is mssing (which I noticed because I have the Chase AGR MC myself), I wonder how many other points/miles cards that are/can be MC are mssing?

Similarly, there are still MCs of personal AA cards from Citi available:

http://creditcards.citicards.com/usc...il/default.htm

(The landing page doesn't show the MC logo, but if you click through to Apply Now, it does.) But again these are not listed on the MC summary liknk you gave.

(To the OP, iowa guy: Remember, you can't apply for a new Citi AA personal card if you opened your last Citi AA personal in the last 18 to 26 months. One you do apply, you should be able to apply for two at a time. See this thread for more on that.)

Barclays Frontier is only issued as a MC

Shoot. I just applied for a Wyndham Barclays card. I received another VISA. What would I have needed to do to get the Wyndham Barclays MASTERCARD?

Do you think I would be able to switch one of my VISAs for a MasterCard? For example, could I swap my Citi Visa for a Citi Mastercard?

Call and ask

Who do I call? Visa or Mastercard?

Can I have both a VISA Chase Sapphire and a MasterCard Chase Sapphire?

Visa/MC only issues the license and the network that enables this cards to work. You would have to cantact the issuing bank to make changes, Chase..BofA etc.

You need to call the bank. MC and V are just acceptance networks, not the credit issuer.