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When banks or airlines offer more than 1 credit card (I guess different levels per-say) if you apply for say the top card and they pull your credit do they decide that you dont qualify for the top card but we will approve you for the middle or lowest card? Or vice versa?
Depends on the card. Some are set up to consider you for it, then move down to the next option. The ones I can think of right now are mostly synchrony cards (e.g., Paypal Extras/Paypal Smart Connect, Walmart MasterCard/Walmart store card). What particular card are you thinking about? I'm sure there's information/discussion about whether it's set up to do that if you search for it here.
It seems like it is mostly something that can happen with store or company specific cards, i.e. Macy's Amex, Paypal MC, Old Navy Visa, etc, etc. Generally, "regular" CCs that aren't tied to any specific company don't tend to "offer you a lower option", outside of offering you a secured in some small circumstances.
The best thing to do is grow and improve your profile to the point where you can apply for what you actually want, not apply hoping for a lesser version.
Chase has a few different ones