Would anyone share the kind of due diligence a BSA Department would do if their domestic bank wanted to open a bank account at a foreign bank in a foreign country? Looking in the Exam manual, it talks about foreign banks opening accounts at a US bank, not the other way around. Thank you.

The very first question I would ask is "Why?".

It would be to facilitate a business customer's transactions. Customer has been with the bank since the bank started, has the entire deposit and lending relationship with the bank and apparently has questioned this type of service.

The customer's transactions can be facilitated by offering products and services from your correspondent bank (e.g., international wires). If there is still a legitimate business need for such an account, the customer should contact the foreign bank and apply for the account, not your bank.

if you are looking for Foreign correspondent banking and BSA

https://www.ffiec.gov/bsa_aml_infobase/pages_manual/OLM_047.htm

If you do not have any correspondent banking it may not be a good idea to do this for just one customer as you may not have the expertise to handle whatever transaction the customer is requesting and additional time and expense to comply with the regulations.

You would also need to check your policy to find out if it is allowed by policy.