Compatibility mode is designed to help users with older products that are not updated. In no case should this help the developer avoid the problems that he might find.
If you absolutely have no choice (for example, a broken dependency such as SharePoint ...) or you want to identify a serious lack of competence, you should not force the user to see your page in compatibility mode.
If you need to support all versions of IE, you must understand how each version works, and be aware of each difference in order to make code that can lead to the same release, regardless of version.
If the idea of โโgetting a "crappy version" (like IE6 and older) sounds really bad for you, I would advise you to set a threshold to focus on compatibility with some older versions, and not with all of them.
EDIT: But if you really need to force compatibility mode, you can use the "X-UA-Compatible" meta tag. For instance:
<meta http-equiv="X-UA-Compatible" content="IE=9" />
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