Ah ha! The key seems to be:
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Before starting the second server, delete all of its config files that may be left over from previous attempts to run it.
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After starting the server, during initial setup, use an incognito browser that is on the same machine as the server. Clear cache in the browser for good luck, then go to http://127.0.0.1:port/web (if you’re using Docker in bridged mode, use the bridge port, otherwise 32400). Don’t use the machine’s actual IP address. This will give you the option at the app.plex.tv login screen to login or to skip logging in by clicking on “What’s this?”
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If you did not log in during step 1, you must add a library during initial setup. If you don’t, the browser just sits there with a spinner at a link that looks like: http://127.0.0.1:port/web/index.html#!/client-setup
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If you did log in, you should see the new server listed under More on the left side
That’s what worked for me!
