I don't know about other tiling WMs, but i3 does let you stack windows. In the default config, super-s makes a vertical stack and super-t makes a tabbed stack.

Most of the time it's easier to keep different windows in different workspaces though. My first five workspaces are always

1. Browser

2. Browser

3. Code

4. Messaging apps (in a vertical stack)

5. Terminals

Pressing the number for the workspace where you keep the window you want is way easier on the eyes and brain then hitting alt tab and examining the pop-up panel to see how many more times you have to hit it.