Is it possible to use Recent Apps to close all open apps less the one I want to stay open?
From the recent apps panel, select the app you want to lock, for example Chrome.

Press the 3 dots menu (above the Chrome panel) to show the lock option. Lock it.

and the small lock symbol shows up.

Now the app is locked and cannot be swiped away to dismiss the app. To unlock follow similar steps. You can clear unwanted apps by manually swiping away.
Alternatively, you can use apps such as Kill Apps, which allow you to customize the list of apps to be killed. Such apps are not usually recommended as Android manages memory space efficiently and such task killers can cause more harm by abruptly killing running apps.
See Recents Screen-Android Developers for more information.