Can I Use Multiple rel="alternate" Tags on Multiple Domains With the Same Language?

[LampsPlus]

Hoping someone can answer this for me, as I have spent a ton of time researching with no luck...

Is there anything misleading/wrong with using multiple rel="alternate" tags on a single webpage to reference multiple alternate versions? We currently use this tag to specify a mobile-equivalent page (mobile site served on an m. domain), but would like to expand so that we can cover another domain for desktop (possibly mobile in the future). In essence:

MAIN DOMAIN would get

The "Other Domain" would then use Canonical to point back to the main site.

To clarify, this implementation idea is for an e-commerce site that maintains the same product line across 2 domains. One is homogeneous with furniture & home decor, which is a sub-set of products on our "main" domain that includes lighting, furniture & home decor.

Any feedback or guidance is greatly appreciated!

Thanks!

[MichaelC-15022]

Typically Google is expecting you to use rel=alternate to tell them about (a) mobile vs. desktop versions, or (b) different language versions.  If it's neither a device difference, nor a language difference, then really all you should be doing is using rel=canonical from the less important/less original version to the more important/more original version.

[LampsPlus]

Very helpful, thanks for the advice Michael!