I don’t know the details of your implementation, but here’s how I would do it. Unfortunately it’s not a very simple solution, maybe there are easier ways that I haven’t thought of.
Firstly, I would prefer to create a separate Item called Payment Method (or whatever you’d like to call it), and then give it a Name (of type text) field where you’d put things like “Visa” or “Amex.” Then have each Payment have a field of type Payment Method (let’s call the field’s name “Payment Type”, just so we don’t confuse the item type name vs. the field name ).
(Using text values might mean you have to make a lot of changes in different places, more likely to make errors, etc. This ensures that if you want to change “Amex” to “American Express” later for whatever reason, you’ll only have to change it in one place. And what if somewhere you accidentally type “Amex” instead of “AmEx”? )
Then, on the working page I would create a custom state for the page or an object on the page, and that custom state should be of type “Payment Method”, and you should also check off that it’s a “list.” For example’s sake let’s call that state “Payment Methods List” (PML)
Create a repeating group of the Payment Method items with a corresponding button for each Payment Method. Then, create a workflow that says when the button is clicked (and conditional on: Payment Method is not in PML), the cell’s Payment Method is added to PML. Create a separate workflow that removes this when it’s clicked again (and conditional on: Payment Method is in PML).
Then, when you filter your Payments and do your “Search for…”, you can say Payments where Payment Type IS IN PML. This gives you both Visa or Amex payments, if you’ve selected them and placed them in the PML.
PS If you want to keep the text version of this (ie not implement a Payment Method Item) you can do the same thing, just make the PML custom state of type “text” instead of “Payment Method.” …but this opens you up to more errors and follow-up changes down the road as mentioned above.