Singapore and
Hong Kong if you can deposit at least 100,000 USD/equivalent (more may be required depending on your profile). You might get a UnionPay card instead of Visa or Mastercard with some banks so check closely.
Some Taiwanese banks accept non-residents, although they seem to prefer business accounts, which come with the usual requirements of connections to the country or region.
Malaysia: the major banks will sometimes open personal accounts for non-resident, usually for VIP banking (100,000+ USD) or if you have a company in Malaysia or Labuan.
Maldives: see
https://www.mib.com.mv/personal-deposits/non-resident-foreign-account
Cambodia: several options, see for example
https://www.offshorecorptalk.com/threads/cambodia-banks.40625/
Bangladesh: see
https://www.offshorecorptalk.com/threads/bangladesh-offshore-banking-units.45419/
Philippines: reports vary but it has historically been easy to open a personal account, although you may now need to register for a tax ID first which may or may not require some sort of non-tourist visa. The situation seems unclear and reports vary between banks, people, and locations. It's not the easiest option but it's not impossible.