history of the Sith is shrouded in secrecy. A thousand years before the events of Star Wars: Episode I - The Phantom Menace, Darth Bane established the Rule of Two; from that moment on, there could only ever be two Sith, a master and an apprentice. The post-Bane Sith operated in the shadows, working to undermine the Jedi and the Republic in a work that would take over a thousand years.
This naturally means precious little is known of the Sith's plans before the Star Wars prequel trilogy, when they emerged from those shadows and left the Jedi reeling after one of their own was slain by Darth Bane. Still, little by little Star Wars tie-ins are beginning to hint at some of their actions. A recent Obi-Wan Kenobi comic book miniseries suggested the Sith monitored the Jedi through the Force, looking for any who had hidden doubts or fears, manipulating their minds and tricking them into leaving the Jedi. No doubt some of these former Jedi were cut down, but others would have been recruited by the Sith.
The latest Star Wars anthology, Stories of Jedi & Sith, subtly hints Count Dooku may have been one of their victims. It includes a short story focused on Qui-Gon Jinn, "Resolve" by Alex Segura. Dooku's former Padawan, Qui-Gon Jinn, was apparently shaken when his master left the Jedi; the book implies it happened shortly after he had been knighted, and left Qui-Gon reeling. The bond between a Master and Padawan is an intimate one, continuing on even after a Padawan has been knighted. Qui-Gon's connection to Dooku was broken when he left the Jedi, and as he reflected upon this experience, Qui-Gon seemed to perceive an outside influence upon his old Master. It's important to note that Qui-Gon had a closer connection to the Force than most, so his view should not be discounted. It's quite likely he was sensing the influence of the Sith.
This rewrites Dooku's story significantly, not least because other Star Wars tie-ins have given a general sense of the timeline. Palpatine is now known to have killed his own Master, Darth Plagueis, shortly before Star Wars: Episode I - The Phantom Menace. That means he was not the Sith Lord when Dooku had trained as a Sith seven years before the saga began, at a time when Palpatine was likely only a Sith Apprentice.
It's fascinating to consider Dooku as a potential rival to Palpatine, although it's difficult to say whether he'd have ever known this. No doubt Palpatine would consider there a certain degree of irony to his later recruiting Dooku himself as an apprentice after Darth Maul's death, especially given he viewed Dooku as a pawn to help him gain control of the galaxy and seduce the Chosen One to the dark side. It's just the kind of approach the great villain of the Star Wars saga would enjoy.