If you want to force fields on plugin tabs you need to edit those plugin tabs in _comprofiler_tabs database table and change their fields column from 0 to 1. This will let you place fields on them, but running tools check or updating the plugin will likely reset that value.
An alternative is you can make a new tab with a Custom HTML field that substitutions in the plugin tab. This would give you a bit more control over where the plugin content is rendered and allow tabs above or below the tab content. See the tab substitution information in the below tutorial on how to do this.
www.joomlapolis.com/support/tutorials/107-use-cases/18353-using-substitutions-throughout-cb