Refresh Some but Not All Data Sources in a Report

Yes, this can be done. Then you need to use Enhanced refresh with Rest API. This can be done from power automate, azure data factory, powershell and so on.

Then you can setup refresh at any time, and you can refresh whole dataset, one table or even a single partition if you have incremental refresh.

You can also have a power automate button in the Power BI report if you want end users to have possibilities to trigger a refresh.

https://powerbi.microsoft.com/en-za/blog/enhanced-refresh-with-the-power-bi-rest-api-is-now-generally-available/

br

Marius