I have a site that has 5 other "alternate" domains that they use. Currently they are doing a serverside rewrite to mask the domain. We are having a duplicate content issue as WP is passing the canonical url for the displayed url. So, if xyz.com is the primary, but abc.com is an alternate url, if it gets crawled as abc.com then abc.com gets set as the canonical url and not xyz.com and so the branded site which should be the canonical url for all alternate domains and therefore all link juice and authority.
Aside from installing Yoasts SEO plugin and page by page setting the canonical url manually I do not see a work around. I am hoping that your multi-domain plugin will resolve this.