Answered the "why" somewhere below, I think you're more concerned about the "how".
Place your tab bar on the left (vertically) and make it wrap to multiple lines (or columns, in this case). I have two columns at the moment, the second one with room for more tabs. Combine this with tab stacking and you have a winner.
You can have your tab bar wrapped to multiple horizontal lines but it's not as efficient given today's widescreen monitors. On lower resolutions (e.g. laptops) it's harder to put as many tabs, but the system is the same and you can still get a decent amount open.
Place your tab bar on the left (vertically) and make it wrap to multiple lines (or columns, in this case). I have two columns at the moment, the second one with room for more tabs. Combine this with tab stacking and you have a winner.
You can have your tab bar wrapped to multiple horizontal lines but it's not as efficient given today's widescreen monitors. On lower resolutions (e.g. laptops) it's harder to put as many tabs, but the system is the same and you can still get a decent amount open.
Give it a try, 4-5 tabs is nothing.