The behavior is mostly caused by an already existing page configuration with route enhancers. First we need to know which page types we need. You can figure that out using the TypoScript object browser (Template > TypoScript Object Browser) searching for a PAGE object and the property or looking into the source code of the affected extensions.
I am using the type 1372255350 from ext:events2 that will be used to find sub categories using ajax.
To get that working we need to edit the site configuration (config/sites/<siteName>/config.yaml). Then we add our route enhancer.
routeEnhancers: PageTypeSuffix: type: PageType default: .html map: events2FindSubCategories.html: 1372255350
This tells TYPO3 to route the page type 1372255350 as events2FindSubCategories.html. Example URL: /page/with/plugin/events2FindSubCategories.html?tx_events2_...