EverBank, Silicon Valley Bank, HSBC US, BBVA to name a few that are defunct or sold now.Mind to hint about one or two of them if you have opened many ?
There are quite some other banks that don't have a strict no policy on that matter. However as far as I understand it it often at the discretion of the manager to open the account or not. See for example Sun Trust (now Truist) or Chase here:
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Also, there obviously are plenty of banks such as Mercury, which open accounts remotely for foreigners without ITIN.
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