Chaosmancer
Legend
So one idea of a fighter gaining supernatural power with levels is found in Brandon Sanderson novels, which are often cited in the new fantasy wave.
In his Stormlight Archive series, The "Knights Radiant" are people whose actions allow them to bond with spirits, known as "Spren". As they grow their bond with their spren by acting out certain "ideals" they gain new powers, even spiritual swords and armor known as Shardblades and Shardplate.
To me its a great example of mundane "fighters" turning into supernatural warriors at the higher levels.
And, importantly, any shardblade or shardplate (if memory serves) that anyone can use is the result of dead spren. And it is far weaker than that which is created to aid a living Knight/spren duo. So it has some fundamental differences to the idea of magical items, because they are less items and more living embodiments of the bond between the fighter and the spirit.