Can I have 2x2 workspaces in GNOME 3?

After you have disabled "dynamic" workspaces using (GNOME) Tweaks and enabled "static" ones (with a fixed number, 4 in this case), install a GNOME extension called Workspace Grid. It

Arranges workspaces in a configurable grid.
Also:

• implements keybindings for left/right workspace navigation (up/down are already implemented)
• updates workspaces sidebar with grid configuration (use Remove Workspaces Sidebar if you don't want it).

From the extension's preferences you will be able to set your preferred layout (e.g. 2x2, 2x3, 3x3 etc.).

You may see its GitHub page for more detailed info.

_{Officially it doesn't support GNOME v3.26 yet, but it should work fine. Otherwise, you may be able to make it work adding "3.26" to its metadata.json file.}

_{Update from the asker:
It worked out of the box without changing anything. Even my old custom shortcuts worked.}

Update 2: Ubuntu 19.04

Currently the extension doesn't work with Gnome 3.32 and it might take a while before (if) it again will, because it's the current maintainer (thanks zakkak) is looking for for volunteers to take over maintainance). Suitable replacement can be Workspace Matrix which has a bit less features, but the main features are present.