In case of templates you can only do up to 1 level of grouping, whereas template category (Standard) itself is initial level of grouping. All you need to do is add multiple templates with the name of Service and all under category Standard Change (pic below). You could have various template categories listed as seen below (Emergency/Notification). However, you cannot do any further grouping for each service using templates.
List of templates with Service under category Standard.
Thanks for the answer, that has helped me understand what is possible