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This is an accepted solution.
By default shopify doesn't allow any sort of customization on checkout page unless you are having Shopify plus plan.
So please let us know your plan first.
So you want this UPS account number information to be retrieved anywhere like on order etc.
Don here from Shopify. :)
As others have stated here, it would not be possible to customise the checkout area at all for security reasons for non-Shopify Plus stores.
You may be able to set something else up for cases where you wish to have customers pay via a UPS account.
It is possible to set up manual payment methods via your admin which you could offer to your customers.
As per the guide above, this functionality would allow you to leave instructions for your customers on how they can check out using this method (you would need to determine how you intend to process orders like this and leave relevant instructions).
Check this out and see if you can find a way to make this work for your specific needs.