Two places in the same series
A television is shared, and the common problem is two people at different points in the same run. Each 9AnimeTV browser keeps its own list and its own episode marks, so the simplest arrangement is one phone per person: each marks their own row with Reached this episode, and whichever phone opens the television session chooses the episode. The television browser can hold a third list of its own for the series the whole room follows together.
Moving a list between screens
My List has Export and Import. Export writes a small file holding the titles and the episode marks; Import reads such a file and merges it, with the later mark winning. Send it from the phone to the television's browser, or between two phones, and the place travels. Nothing leaves the browser otherwise; there is no account.
Which episode to mark
Mark the episode you finished, not the one you are about to start, so the highlighted row on the season page is the last one everyone saw. When the room disagrees, the season page lists every episode with its air date and a one-line summary, which settles it faster than a debate.
Subtitles for the back of the room
On a shared screen the subtitle size matters more than anything else on the page, and the sub and dub page explains where to set it on each service.