You can open more than one account at the same bank if the bank's products and procedures allow it, such as a current account, a savings account, or accounts in different currencies.
Key points
However, before opening them, consider the purpose of each account, as each may have its own fees, minimum balance requirements, and terms.
If the second account has no clear purpose, its cost and management may be more of a burden than a benefit.
The figures, fees and limits in this answer vary by bank and change over time — confirm them with your bank or the official source before acting.