It is possible - I have done it - but there are lots of things to keep in mind for success. The most important, in my view, is to appreciate that your visible links structure and navigation does NOT need to be reflected in the URL.
Said another way, you can create categories and subcategories for the human visitor that are not reflected in the apparent "file path" of the URL. This can allow you to keep the same URLs, and it's in changing the URLs where established rankings can get broken.
Start by knowing where your strongest pages are - the best backlink strength and the nest entry pages, whether from the SERPs or direct navigation or whatever. Those are the URLs you try to avoid changing. And if you do need to change them, make sure to use a 301 redirect.