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

See also:

• New Tab Tools: https://addons.mozilla.org/firefox/addon/new-tab-tools/

Thanks for the support. I used

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

and installed the add-on. Now I have sixteen links set up. Very handy!