There have been a lot of threads here about what sort of villain the Mandarin should be.
As far as construcing a villain goes, I suggest watching this about Star Trek villain Gul Dukat: (spoilers for Star Trek DS9)
With all this in mind, in my own head the Mandarin should be shown to have as much in common with Tony Stark as possible.
First I would have him stop wearing his rings in battle. But this doesn't mean he should stop having them. In my scenario, he should be using the rings to create other weapons he would then use in battle. He should use the rings in conjunction with other materials (iron, maybe vibranium, maybe something else) to create swords, daggers, shields, even old school armor. Swords and other weapons were made by pounding, heating and quenching metal, something he can do with his rings. Doing all this would give the Mandarin an even more "old school" vibe. (Being old school is one of the Mandarin's best draws.)
If these weapons had other properties (energy projection for example) he would still be a good match for Iron Man. But more importantly for the purpose of changing the character, the weapons could be used by other fighters. That would make the Mandarin a supplier of weapons for a part of the super-villain world the same way Tony is now a supplier of weapons for other superheroes.
What are your thoughts on this?
I don't know if it should be a totally new character or a way to reinvent the old Mandarin but that's one of the directions that I might choose.
One of the interesting ideas that came out of Iron Man 3 was "Mandarin/Aldrich Killian" being a kingmaker.
Currently, in the former USSR countries (Russia, Ukraine, Central Asia ...), oligarchs are kingmakers, choosing to finance & support one political candidate or the other. Some of them are relatives or close associates of government officials or even government officials themselves (thus, "mandarins").