(**Warning of Spoilers for Superman: The Man Of Steel issues 17 and 18 , Superman: In the Name of Gog , Superman: Hunter/Prey (1994), Superman #175  and Superman: The Doomsday Wars [1998 to 1999]).
Doomsday debuted in Superman: The Man of Steel issues 17 and 18 (1992) as an unknown force of nature due to a last-minute cancellation of a planned year of Superman comics (Superman/Doomsday  Special Feature Requiem & Rebirth: Superman Lives!). The creative teams of the Superman titles of that time created Doomsday as a monster meant to kill Superman. In other words, they made him a character with arguably zero defining qualities. Yet, he has endured. This is due in part to one of his creators, Dan Jurgens, continuing to use Doomsday in mini-series like Superman: Hunter/Prey and Superman: The Doomsday Wars. Thus Jurgens opened the door to other stories featuring Doomsday.
Now, instead of going into these other stories in detail, we will look at whether Doomsday can actually be a well-rounded character and whether new stories can include him. To start, we need to look at what characteristics he could have added to his persona. For example, in Superman Hunter/Prey we get to see how he views Superman as his creator, Bertron. Now this is supposedly because Bertron is an alien who developed Doomsday, via experimenting with forced evolution, on a prehistoric Krypton. So, maybe a story that is visually told from Doomsday’s point-of-view could be done to explain this further.
Another characteristic that could be developed further is explaining how much of Doomsday is basic instinct versus conscious will. Superman: The Doomsday Wars suggests this very thing when Brainiac takes mental control of Doomsday, yet Doomsday’s mind fights him off. This could lead to stories where either Doomsday or an alternate version gets a Green Lantern ring.
[Cover of Superman #175 December 2001 Pencils by Ed McGuinness and Letters and Colors by Liquid.]
Finally we go to Superman: The Doomsday Wars, Superman #175, and Superman: In the Name of Gog as examples of an intelligent Doomsday. The foremost suggests he would be more effective at fighting. However, since Brainiac controls Doomsday, and the superheroes who fight him get taken by surprise, we shouldn’t fully count this story as proof of this characteristic. The latter two examples actually show Doomsday as a weaker fighter due to thinking about pain and self-preservation. Also Superman: In the Name Of Gog shows how he could be a possible anti-hero. So I suggest that he could be a reverse of Marvel’s Ultron, with a mix of the Hulk’s power set, in terms of evolution and inclination for certain longer-form stories (Age Of Ultron  and Hulk: The End ).
Whether we will ever see these or other developments happen for Doomsday, only time will tell.