Yes! You can absolutely watch sessions across multiple domains. FullStory can record sessions across subdomains, but the domain for each must be the same. For instance, if your recording snippet was present on www.example.com and subdomain.example.com, FullStory would record across both domains into one single session.
Note: In most cases, FullStory will use the TLD+1 (top level domain + 1) to join sessions together. E.g. www.example.com has a TLD+1 of example.com. However, there are some sites which allow public hosting of content by multiple companies/individuals, for example Github pages with a domain of github.io. In these cases, the subdomain of the public suffix will be used to group sessions together. A list of public suffixes can be found here.
For domains that aren't related (such as example.com and anotherexample.com), FullStory would split the sessions in two; however, there is a way to string these sessions together. First, you’ll need deploy the same FullStory recording snippet for each site as to record all sessions into the same account (FullStory is unable to tie sessions together across multiple accounts). You can find your recording snippet under Settings > FullStory Setup.
Second, you’ll need to implement FS.identify on your site in order to pass along a unique user id (UID) for the session. This UID will be used to string the sessions together later. As a reminder, you can not track anonymous users across domains, but you can track identified users across domains.
These cross domain sessions are automatically split into separate sessions, but if you search for events that tie the two sessions together, they will appear as a single session Clip during playback. You'll be able to watch this clip to see the activity across domains, but will notice a "break" in the timeline, indicating the activity is within a different session.