Not sure what GNOME version are you using, but there are some plugins out there like gtile and ShellTile.
Found this page where the tile shortcurts are listed, but I do not use GNOME to test it. Maybe there is a disabled shortcut entry for this somewhere.
On Cinnamon (I use it) the window tiling shortcuts are default as windows and you can also "snap" a window, so it becomes something similar to the "always on top" feature, but having its own space. You can see what it is by this video.