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How many of them are out there, at least in the USA? M/C, Visa, Amex, Discover?
Payment Networks you mean? As far as I know, you already listed them all. Maybe Diner's Club still? @FinStar may know more.
@W261w261 - are you referring to processors like PayPal, Chase, Helcim, Square or National Processing, for example? There's 1000's of them depending on the type of services you're looking for (e.g. low or large transaction volumes, lowest fees, high risk merchants, etc.). Payment networks-wise, you've pretty much listed the major 4.
If I understand the question correctly, the OP is asking if there are more than the four "payment processing networks" listed in the original post (i.e. Visa, MasterCard, American Express, and Discover). I believe the answer to that question is, "yes", kinda-sorta.
In addition to the Big-4, here are some other payment processing networks I have heard of in my travels:
Chapter 13:
I categorically refuse to do AZEO!








Yes, I was referring to the visa, m/c etc. I remember Star from years ago, when some debit cards would incur an extra fee if they were/were not on "Star." I never really understood those.