Is the hyphenation correct in the following:
They currently operate a number of credit-card based and other loyalty programs in the US and elsewhere around the globe.
My response: "credit-card-based" all modifies "programs," so hyphenate the whole thing. It's confusing only because the noun "credit card" is two words; if it were, say, "money-based programs" it would be obvious that there's a hyphen before the "based".
If you want to be *really* technical about it, because of the "stacked" hyphens, in this case the credit-card hyphen would be a regular hyphen but the -based would be an en dash.