I read this trilogy 20-ish years ago. It was a military science fiction story about a group of soldiers who were augmented. I think it was genetic enhancements, as the main character developed beyond expectations (telekinesis and the like). I can’t recall many details of the story or the conflict even, but I remember it ending with the main character becoming the President of the Galaxy or something like that. I know this isn’t much to go on, but that’s why I am having difficulty tracking it down.
This sounds like the Childe Cycle* by Gordon R. Dickson, specifically the first novel, Dorsai! (1960). The main character, Donal Graeme, is a mercenary from the titular military planet Dorsai, and the book follows his career through positions of increasing importance, with the chapters mostly labeled by his rank or position at each stage. He progressed from being an unemployed mercenary, through low-level soldiering and increasing levels of command, culminating in a position as supreme military chief for the galactic civilization. At every stage, he exhibits extraordinary abilities, culminating, late in the book, with telekinesis and possibly other psychic abilities (although he keeps these psi abilities hidden).
The plot summary, per Wikipedia:
The book is about Donal Graeme, warrior extraordinaire. In the Childe Cycle universe, the human race has split into a number of splinter cultures. Donal is a member of the Dorsai, a splinter culture based on the planet of the same name, which has specialized in producing the very best soldiers. Since each splinter culture specializes in a specific area of expertise, a system of trade labour contracts between the cultures allows each planet to hire the expertise they need. The Dorsai, inhabiting a resource-poor world, hire themselves out as mercenaries to other planetary governments. Donal has great ambitions, and the book follows his rise in an episodic manner. The book begins as a straightforward tale of his career and then becomes something else, as it becomes clear there is something different about Donal Graeme himself.
Donal quickly comes to the attention of William of Ceta, a powerful politician. First he is asked by Anea Marlivana, a so-called Select of Kultis, to destroy her contract binding her to William. Instead Donal returns the contract to William and gains a post in his military. Donal next catches one of William's officers in a plan to fake some heroics, compromising Anea in the process. Taking command himself, Donal has the officer shot for violating the Mercenaries Code. Leaving William's command, he embarks on a series of operations in different conflicts that mark him as an innovative genius.
In the final chapters, Donal achieves something previously thought impossible: the invasion and conquest of a planet, William's home world. During William's capture, Donal finds that William tortured and killed Donal's brother. He turns one of his new-found abilities on William, inducing agony, then enters a coma himself. On waking much later, he frees William from the "curse", saying that William will be needed. There is a conference to address the fallout from Donal's actions, resulting in the formation of a Federation with him as leader. Anea is now Donal's consort, but Donal has changed into something beyond the normal human. He calls himself "an intuitive superman", gazing outward at the stars.
The novel has been published in several forms. It was originally serialized in Astounding Science Fiction in 1959, then edited down for book publication the next year. After the author's death, it was published in an omnibus edition, alongside the fix-up The Spirit of Dorsai. Another omnibus, Four to Dorsai! contained four novels, and that might be where you read it.
Books from the Childe Cycle (including Dorsai! itself) have previously been the answers to these story identification questions: What's the name of a book about super endurance through relaxation? and Seeking a novel in which the hero recognizes the spice smell of oncoming enemies
*Although the intended "cycle" was never actually completed before Dickson's death in 2001.