Make all opened document tabs visible
One of the built-in option to do so: use pinned tabs. http://dailydotnettips.com/2016/01/21/persevering-and-separating-the-pinned-tabs-in-visual-studio/
If you don't want to read a external page just for setting:
Tools -> Options -> Environment -> Tabs and Windows -> Show pinned tabs in a seperate row
It's not completely what you want, but it's free and may be useful.
Maybe it's not exactly what you search, but here is a way to at least get a second row for pinned tabs.
Effectively get you more space for opened files:
Tools -> Options -> Environment -> Tabs and Windows -> Show pinned tabs in a seperate row
Visual Studio has this extension taken from msdn.microsoft.com tested and worked
Simple installation: download, doubleclick to install, restart VS IDE. Then open all the tabs you want they all will be displayed and No hidden.
https://visualstudiogallery.msdn.microsoft.com/EBF6137E-AA2D-4DC9-860A-F04168F11CD7
Dung Le.