Do banks like Wells Fargo, Bank of America, etc. have the ability to purchase stock for account holders in the?
Such banks have divisions, subsidiaries, operational areas that are registered broker/dealers and separated from the bank in both management, accounting and organization.
The separate areas are registered with the SEC and are members of FINRA and are subject to their rules & regulations, they are not controlled by or regulated by banking regulators.
These B/D operations can and often do service bank customers only after those banking customers open an account with the brokerage operation