Is rel=Canonical added with rel=alternate ok to do so?

We launched a mobile site a couples months ago following the parallel mobile structure with a

The week later my crawl detected thousands of dups which I resolved by implementing canonical tags on the mobile version and rel=alternate onto the desktop version. The problem here is that I still also got Dups from that got generated by the CMS.



One of the options to resolve those is to add canonicals on the desktop versions as well on top of the rel=alternate tag we just implemented. So my question here:

is it dangerous to add rel=canonical and rel=alternate tags on the desktop version of the site or not? will it disrupt the rel=canonical on mobile?