I am aware that doing this is possible in Android (here is a related question). However, currently I am very puzzled about whether it is even possible to do this on Windows Phone.
Having had a look at the APIs, it appears that the call GUI has to be in the foreground (so launching it as a background task will not work). I've also considered if a popup can be created on top of the call interface.
This is a request (and one of the most important ones) of my client so while I strongly disagree with the idea of overriding the default call interface, this is more or less the requirement.
Thank you very much in advance!
You could custom UI for call app, such as dialer pad, dialer button. However, you could not modify the Call interface, it is system level. For more you could refer official code sample.
This is a request (and one of the most important ones) of my client so while I strongly disagree with the idea of overriding the default call interface, this is more or less the requirement.
For your requirement, you could refer CompactOverlay mode. When an app window enters compact overlay mode it’ll be shown above other windows so it won’t get blocked. This allows users to continue to keep an eye on your app's content even when they are working with something else. This is introductory blog. And this is ApplicationViewMode enumeration class.