Hi Taysir,
Great question! Honestly, I'm not confident what would happen if you add the rel=canonical and rel=alternate tags to the desktop version (and whether that will disrupt the rel=canonical on mobile or not). My advice is to test it out on a few select pages (I would recommend not testing your most important/highest revenue driving pages first, but on less critical pages) and see how the search engines deal with these pages. If the duplicates are removed and traffic to the mobile site isn't affected, then I would start scaling the rel=canonical out on other pages. However if you do see an issue with the combination of rel=canonical and rel=alternate on the desktop version, then it may be worth fixing the CMS, so that it no longer creates these duplicate pages.
Best,
Stephanie