Incidentally, I am running 1920x1080, so screen resolution is not the issue.

Aspect ratio could be an issue...

If you zoom out on the page (e.g., hold Ctrl and tap the - key once or twice) you should be able to get more tiles on the page. However, some users have reported that this doesn't hold, and others find it unsatisfactory that this also shrinks the search box. An alternate solution is to use an extension to tweak the page, such as:

https://addons.mozilla.org/firefox/addon/new-tab-tools/

You can zoom out the about:newtab page to resize the tiles and have more tiles fit on the page.

• View > Zoom > Zoom Out; Ctrl and -
  "Zoom Text Only" shouldn't have a tick

This will affect all elements on the page, so text get smaller as well.

Make sure that only one tab with the about:newtab page is open when you change the page zoom. Toggle the browser.newtab.preload pref to false on the about:config page in case of issues with remembering the page zoom of the about:newtab page.

You can open the about:config page via the location/address bar. You can accept the warning and click "I'll be careful" to continue.

• http://kb.mozillazine.org/about:config