How can I effectively utilize more than 4 skills per category in my build?
Solution 1:
There is indeed a way to have a second set of melee abilities. You can switch between the two wheels by activating the melee ability wheel (e.g. LB/L1 on consoles), and pressing the switch button (D-Down on consoles).
The second wheel is locked behind story progress, though. I've explained how to unlock this below, but be wary of spoilers!
Once you obtain the main story quest Memories Awoken, you will unlock the Forge. This allows you to upgrade the Spear of Leonidas using Mysterious Fragments, which are obtained from killing cultists. After completing this quest, your spear will be level 2, and you will receive a quest to upgrade your spear to level 3. Once you have upgraded it to level 3, you will unlock the second melee ability wheel.