No you can't. Although it is possible to access both the old and the new CS portal, this can only be done using two different user-ids (you can, however, use the same URL for both portals). Keep in mind though that in the old CS portal you will not be able to create cases. Also, as soon as the new CS portal goes live in your country, neither installed product data (the assets), nor contracts nor cases will be updated in the old CS portal.
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