Iron Crown Enterprises (ICE) held the rights to produce a roleplaying game set in Middle-earth from 1984 to 1999. One of the company's founders, Pete Fenlon, expanded the map of Middle-earth to include the east and south. These lands aren't canon; and not much was written about them for the game. However, some of these places were used to provide origin stories about the Nazgul, one of whom was female in the rpg.
Brief descriptions of the lands on the Wayback Machine
I've been fascinated by how different Pete's map turned out to be from Tolkien's own sketches of Arda as seen in The Shaping of Middle-earth. Tolkien's Harad is actually another continent that corresponds roughly to Africa. Tolkien also depicted a separate South Land (Dark Land) that would have likely broken up into Antarctica, Australia and Indonesia. Karen Wynn Fonstad drew upon Tolkien's sketches for the revised edition of her Atlas of Middle-earth.
http://www.tolkienforums.com/Maps/Map%20of%20Arda%20after%20Change.jpg
I have an old edition of the atlas. I need to get an updated version, which covered the east in more detail.
I've dabbled with the idea of going off the lands in the books and setting a couple of campaigns in the lands invented by Iron Crown Enterprises.
If you have the material then you might as well put it to use. Adapting it to TOR might be the biggest challenge unless you are using the MERP rules.
I'd either use MERP or AD&D. Note that some of the campaigns I thought about doing were my own ideas which I wrote down but never tested. My notes are system-neutral, so they can be used for any game system.
The easiest way to use the material would be to use the default time setting for MERP, but the team always suggested at least some ways of using the adventures and supplements in other time periods.
My current game on Tabletop Simulator is set in TA 1640, which is the default year for MERP. My other campaign is set in TA 1670, since it's a sequel to my original game.
If we're going to go off the known map, we can pretty much decide what year to set the game in. I used stuff from the History series as a basis for my Palisor setting and the stuff from ICE for my Shelflands setting. The latter one was based on the ICE stuff anyway.