I have tried CSE.next on multisite setup, where I have two VCD sites paired on system and organization level.
So, sites are rs-bg-1-ec and rs-bg-2-ec and I can see VDCs and VMs from both sites in VCD.
Also, in CSE UI plugin on rs-bg-2-ec site I can see k8s clusters from both sites:

If I click on cse4-rs-bg-1-test-1 link, it will open rs-bg-1-ec site in new browser tab, but it will not accept my current SSO login and I will need to login again to manage my cluster. Annoyance, but bearable.
The real problem is, if I login to rs-bg-2-ec site, and go to another site by SSO, and then open CSE UI plugin, it will not be able to show any clusters, it will display message "Error: Failed to fetch Kubernetes clusters"

There is 401 Unauthorized HTTP request to rs-bg-1-ec site's /api/session url and there is a "CSE UI: Error fetching sites" message in browser console.
Note: Similar problems were noticed in CSE 3.1 when using multisite setup.