I believe your best bet would be to use the "Cross Domain Tracking Using First-Party Cookie Sync and Iframes " functionality. This will allow you to share data across domains you own and operate, and are managed by Tealium.
My assumption is that you'll want to persist, for example, the Google Analytics _ga or the Tealium utag_main_v_id IDs between domains, and this will allow you to do so. It does require a little more effort than a typical Tealium deployment, especially since each domain will need to host a new file that can set a 3rd-party cookie, then will become a 1st-party cookie. The details of the above article should cover this part in more details.
Please let me know if this is what you're looking for, or if you need more guidance.
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