There are two general trends with established jurisdictions lately (HK, Singapore, UAE etc.).
1. Making deposits, buying financial products (investments or insurance)
2. Using a local person directly or via POA to open the account and later include you into the company
For HK last account we set up for a client involved hiring a chinese person with an actual business in Shenzhen, he registered the company and applied for an account using his actual business as proof of substance, account got opened, the client was introduced into the company as 100% shareholder and second director, chinese person got written off within 3 months. Bank was notified every step of the way, they did run an additional KYC on the second director, but account staid functional and KYC was not too envasive. For UAE the beneficiary registered the company and issued a POA to a local UAE resident to open account for him, helped with the bank since they need the residence number and the client could not spend 2-4 weeks in UAE processing his residency.