Does three dots in linear make sense "more" in web applications, i have seen them only in mobile design?
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They almost make as much sense as the word "more" ...
As with any icon, I personally have taken to do what you're doing everywhere else in that design: use an icon with a word next to it.
Or "Menu" followed by the hamburger icon.
Alternatively, use a down arrow. That one has worked for years, and is still seeing heavy use across (web based) applications.