Button that can Auto Size as well as be Stretched

Is there a way to create a Button with a Caret that can Auto Size based on text expanding…

…as well as be resized manually and then continue to Auto Size based on text expanding?

I can make one or the other but not a button that does both.

I realize that resizing a button manually sets it’s width to FIXED, but maybe there is a work around/hack or another way to build a button to allow this? Is there a way to look at this problem laterally?

Thank you

This is impossible. By manually resizing, you make your object a fixed width/height.