It is often said that Tolkien had only finished 1/3 of his life's work before he died and looking through all his books and notes shows much truth to that. Virtually nothing was written about what happened in the east of Middle Earth during the events of Tolkien's work, though from what we do know, it indicates something big was happening there.
The thing is, is it worth exploring?
First, a little study of the world and people who live in the east.
The problem when describing the geography is that most of it comes from the Years of the Trees and the First Age of the Sun, meaning that most of it is likely gone by the time of The Hobbit and LOTR which take place near the end of the Third Age of the Sun. This is because events like the sinking of Beleriand and the changing of the world (aka, when Arda was turned from flat to round) altered the geography of Arda greatly.
As such this part will be split into two sections for each era.
During the Age of the Trees and the First Age, East Middle Earth was known as Palisor and right in the middle of it, there was the giant inland sea of Helcar. Cuiviénen lay on Helcar's eastern coast and was the birth place of the elves.
Behind that lies the wild wood which wasknown for its beauty. To the south east lies Hildórien, the birth place of humanity. Man would live here for a longtime until Morgoth arrived, with many fleeing to the west while others staying to worship him.
To the north east lies Orocarni, a mountain range that connects to the Iron mountains where Utumno, Morgoth's Great Fortress once stood. Lastly, there is possibly the Yellow mountains, but they could actually be part of South Middle Earth.
Helcar no longer exists, as it was drained by Morgoth. Cuiviénen, the wild woods and the Iron Mountains were also destroyed, with all that remained becoming the Iron Hills. However, Orocarni still stands and Hildórien may also still exist.
East Middle Earth had at least two nations, Rhûn and Khand. Though nothing is known about Khand, in west Rhûn lay the Sea of Rhûn and next to it was Dorwinion, a place known for its grand Gardens and making the finest wines in Middle Earth.
Like its geography, we don't know much about the people who live there. Given what we've seen in West Middle Earth, it is likely the east has its own mix of unique beasts and races. But because of the lack of information, we can't say for sure.
The Easterlings are probably the most well-known group of people who live there. Easterlings is the name originally given to two tribes of humans that served Morgoth in the first age, likely descendents of his worshipers from Hildórien. They were called the Sons of Bór who were wiped out and the Sons of Ulfang.
In the Third Age, the Easterlings now consist of a mixture of humans and dwarves and are several tribes that live in the nation of Rhûn. Many of them still worship Morgoth and work for Sauron such as the Wainriders (the ones you see in the films) and the Balchoth who were known for their chariots.
However, not all Easterlings were evil. It is mentioned in his notes that some tribes fighting against the Wainriders and those who live in Dorwinion openly trade with the Free people and stayed neutral.
The Variags are the men who come from the nation of Khund. Nothing is known about them except that they supplied Mordor's horses and that they fought in Sauron's army during the siege of Minas Tirith.
The name stems from Varangians, a group of Vikings who ruled the ancient Kingdom of Kievan Rus'. This could suggest that their culture is based on the Vikings though oddly, nearly all media seems to portray them as either Japanese or Mongols.
As mentioned before, the elves originally came from Cuiviénen. But when Morgoth came, most of the elves fled to the west and took the great journey to become Eldar Elves (the ones you see in the movies) which gave them super powers, but also screwed them over when Morgoth destroyed the source of their power. However, one group of elves, the Avari, stayed behind and though some were captured and became the first orcs. The rest flourished in the east and were the ones who taught humans language and culture as well as the inventors of wine in Middle Earth.
The Eldar Elves hate them (Dark Elf is actually a slur) and consider them barbaric and uncivilized. But unlike their Eldar cousins, they did not have to leave Middle Earth thanks due to them never going on the Great Journey.
Lastly, despite the name, Dark Elves aren't evil (well, except for the ones turned into Orcs) and actively fought Morgoth.
Again, like mentioned before, some Dwarves have either conquered or assimilated themselves into the Easterlings. But there are also Dwarf Kingdoms scattered around the place, most noticeably in Orocarni.
Alatar and Pallando, known as the Blue Wizards for their sea-blue robes were spirits who served Oromë, the valar (god) of hunting. They were chosen to become two of the five wizards who would go to Middle Earth to help defeat Sauron.
Nothing is mentioned about their personalities but from what we see of the other three Wizards, their personalities would be very similar to the Valar they serve. For example, Radagast is a servant of Yavanna, the valar of nature so in turn, he is also dedicated to nature. As such, it is most probable that the Blue Wizards were highly trained hunters, trackers and their magic was based around that.
Both went to the east to aid those who fought against Sauron but both would eventually vanish. What happens exactly is unclear, but from Tolkien's later notes, Pallando was involved in an event that changed the course of the war but would be unnoticed by those in the West.
Probably the biggest problem you would have is what would be the villain and what would be the plot?
There are many interesting possibilities for villains offered in the source material itself. First of all, Morgoth's remaining soldiers and lieutenants. Though most perished with him and Sauron went on to become a dark lord in his own right. There are still a few unaccounted for such as Lungorthin, a powerful Balrog (think about three times more powerful than the one in Moria) who was chief of security of Angband.
There is also the Nameless Things. During the world's creation, Morgoth (known as Melkor back then) discord resulted in the creation of these powerful and intelligent abominations who care for no one. One of these creatures was Ungoliant, a massive mutant spider who tricked Morgoth into thinking she was his ally before betraying him.
Or you could always create your own. Nothing would stop you from creating a threat unlike anything established in the books. Even Tolkien himself was exploring new threats in an unfinished book.
The same can go for plot as well. The plot doesn't have to be another LOTR or be similar to the previous films. You can explore new ideas and plots that weren't covered or weren't possible in the novels.
There is also of course the event Tolkien hinted at. Something that happened in the East that changed the course of LOTR but was not noticed in the West. What could it have been?
In my 0pinion, yes.
It would definitely be different from the Hobbit and LOTR, moving away from the standard European mythology and exploring Slavic, Chinese and other mythologies that don't get explored as often. It would also be a great way to diverse the Fantasy genre that is all too often solely focused on white people, usually reserving POC as minor characters and/or villains.
Plus, you would already have the Middle Earth brand already in place. Which make it far more easier for it to be understood and accepted in the mainstream. Something that other fantasy universes struggle at outside of fantasy and geek circles like Dragonlance and the Wheel of Time.
But would general audiences be interested in such a project? I would think so.
Remember, what annoyed audiences about the Hobbit films was that they felt overblown and didn't do anything new. If you used this as a way to tell an entirely new story that didn't have to be tied down or didn't fail to stand on its own (I should point out I actually enjoyed the Hobbit films at this point). I think audience would accept it and enjoy.