According to the Basel Committee on Banking Supervision, banks should deal with high-risk customers by:

According to the Basel Committee on Banking Supervision, banks should apply a risk-based approach to customer due diligence, which means that they should adopt enhanced measures for higher-risk customers and simplified measures for lower-risk customers. Enhanced due diligence (EDD) may include obtaining additional information on the customer’s identity, source of funds, business activities, beneficial owners, and expected transactions, as well as conducting more frequent and intensive monitoring ofthe account activity. EDD is especially important for customers who are politically exposed persons (PEPs), who are from or have connections with high-risk countries or jurisdictions, or who are involved in high-risk industries or sectors. Therefore, performing EDD including enhanced ongoing monitoring of the account activity is the correct way for banks to deal with high-risk customers.

 Basel Committee on Banking Supervision, CAMS Study Guide, 6th Edition, Chapter 4, page 121.