Our team has worked with both Snowflake and MS PowerBI to find a solution to this issue, trying out the different workarounds suggested (both at the Snowflake config and also in PowerBI). Sadly, it boiled down to Microsoft saying that their ODBC driver for Snowflake does not handle MFA/DUO connections properly, and asked us to file a product enhancement request.
Moving forward, we have decided on this workaround:
a) Checked and identified which IP addresses are used by the PowerBI users to connect to Snowflake
b) Created a Network Policy in Snowflake that would limit user connections to those IP addresses identified in (a) ---> aka IP pinholing
c) Disabled MFA on those PowerBI users
And since PowerBI users do not have MFA enabled in their accounts, they do not receive the multiple DUO prompts anymore.
If I connect to Snowflake as per https://docs.microsoft.com/en-us/power-bi/connect-data/desktop-connect-snowflake (using Snowflake as my IDp - without Microsoft AAD integration), and MFA token cac...