Is there a way to modifiy this page (Sites in Office 365 that shows you the sites you are following, the suggested sites and the promoted sites)?
I can't see an option like Edit page or something like that for this page
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If I understand the problem correctly, what you wanted is to manage the promoted sites and sites you are following.
For promoted sites, only administrators can manage it. It is global to all users. In the administrator view, you will find the boxes(sites) to be editable.
For sites you are following, you can un-follow sites by clicking on Stop Following button or go to the site and click Unfollow (located on the upper right corner of the site). Similarly, for sites that you want to follow, simply navigate to the site and click Follow.
This link will give you a more detailed guide for managing promoted links. On the other hand, this link demonstrates on how to follow or stop following sites. I believe there is no way wherein you can manage the sites in a tabular (like a list) manner.