We've internally hardcoded it to 20 in the meantime, and it seems to work pretty well.
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Having 20 tabs is bad design, what problem are you trying to solve?
https://secure.phabricator.com/book/phabcontrib/article/feature_requests/
For context, this is for organizing tasks at MemSQL for the database engine. We use projects to track releases and want to use a dashboard to build an overview of how each component of the engine is doing. One of the views is a query over all failed tasks, split up by engine component. I built a visualization in dashboard for this today, and we ended up with 12 components (1 tab per component). It looks/works quite well with 12 tabs.
+1 for increasing the limit. We built a dashboard that breaks down things by individual team members. I don't have a team of 20, but more than 6 is better!
I believe the main hangup was have Javascript collapse the tabs into a menu as the page shrunk. (Responsive layouts).
We're also pretty happy with the current behavior when the page is too small - the tabs just neatly display over two rows instead of one. It enables jumping to a specific tab very quickly in the interface.
I agree with Ankur that the current stacking behavior that happens when you have more tabs than can fit in one row looks fine. The only visual tweak I would suggest is injecting a border between each row. I also prefer the horizontal layout even at small screen sizes rather than stacking the tabs as it currently does. Here is an example of multiple rows: