How to arrange windows in e.g. 3x3 pattern?

Windows cannot create such screen snap areas. The most it can do is set a 2x2 grid, as you have found out.

You need a third-party product that is flexible enough to define any screen setup and is easy to use.

The best product I have found in that domain is the completely free GridMove, which has a long list of capabilities:

• 3 different interaction methods to suit everyone’s likes
• Several pre-made grid templates that can be easily swaped
• Ability to set windows on top and maximize them vertically or horizontally
• Full keyboard support, which can organize windows with one hotkey press
• MultiMonitor Support
• Customizable hotkeys
• Customizable interface
• Possibility to create dynamic custom grids
• Complete help file

A tutorial GridMove Grid Making Tutorial can be found on their forums, where the users help each other with complex grids. For example :

An alternative is AquaSnap which is choke-full of goodies, but the free version does not have the more advanced features such as Mouse shortcuts and Window tiling. For that, one requires the Standard version at $18.

Microsoft now provides a free tool to do this, called FancyZones, one application in a larger suite called PowerToys. There are some great instructions at onmsft.com. There is even a setting to override the default behavior of the Windows-arrow hotkeys to move windows among your custom grid.