Do credit card companies communicate with each other if there is no credit check or limit increase?

by Center for American Progress Action Fund
Question by fantapattaya: Do credit card companies communicate with each other if there is no credit check or limit increase?
I have 3 credit cards.

2 of them I'll need to stop paying for now, but I'm not going bankrupt yet.

Can I keep the third credit card if I keep paying it?

Or will the 2 other credit card companies call them and tell them to cancel me also?

I would like to add that I will NOT ask for aditional credit from the existing card

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