As an aside, if using four ability scores, I am happy with the following arrays. Choose either.
• +3, +2, +1, +0
• +2, +2, +2, +2
The numbers are somewhat high because I prefer to avoid dealing with negative numbers.
As per the recommendation of
@Campbell in a thread on 4e-like games, I looked (briefly) into a game called "Unity," which really should have thought longer and harder about its brand name. It uses four ability scores: Might, Agility, Mind, and Presence. You start with your pick of an initial spread of abilities - that I can't recall off the top of my head - your pick of where to place a +1, +0, -1, and +2. Then your race provides an intial spread of abilities: Humans, for example, receive +1, +1, +1, +1 while another race may receive +2, +0, +1, +1. Exact details escape me, but it's something along those lines.
I am interested in seeing your considerations about ability scores.
When considering ability scores, Celebrim offered a poignant point that I will again raise here:
Ultimately, the decision to add or remove ability scores from a system has less to do with whether a system works, than it is a reflection about what the designer really cares about in terms of verisimilitude and character conception.
I would also add that it is additional a reflection about a designer cares about in terms of the system.
Cypher System uses three stat pools: Might, Speed, and Intellect. These stats, however, operate different than they do in D&D and other games with ability scores. Here, they represent the totality of a person's staying power, doubling as something akin to an HP system and ability/magic fuel. A melee attack ability may require that you expend 2 Might from your 17 Might pool total to perform the maneuver, but then require 3 Might total if you spend one level of Effort to lower the difficulty by 1 (or lower the TN required for a success on a d20 by 3). So the resource mini-game shifts to managing the stat pools and your abilities. Could Monte Cook Games have expanded the number of available stat pools to reflect other stats? Sure, but three stats keep the complexity down.
Blades in the Dark also uses an "ability score" system that I find intriguing. There are 12 actions that are divided between three attributes: Insight (Hunt, Survey, Study, Tinker); Prowess (Finesse, Prowl, Skirmish, Wreck); and Resolve (Attune, Command, Consort, Sway). The game entails a dice pool system. (Success on a 6; Complicated Success on a 4-5; and Failure on a 3-1.) The number of points you have in an action reflects the number of d6 dice you can roll to increase the odds of success. So as you progress your character or decide stats, you may want to invest deeper into an action for greater success.
BUT you use your Attributes (Insight, Prowess, Resolve) for resistance rolls to mitigate consequences of failure. How many dice do you get for your Attributes? That's determined by the breadth of actions you have invested within that attribute. If you have 1d6 in Finesse, 3d6 in Prowl, 0d6 in Skirmish, and 0d6 in Wreck, then you have 2d6 for your Prowess (essentially a combined Constitution/Dexterity saving throw) resistance rolls. But if you had 1d6 in Finesse, 1d6 in Prowl, 1d6 in Skirmish, and 1d6 in Wreck, you would have a 4d6 for your Prowess resistance rolls. So there is a tradeoff between your breadth of your attributes vs. the depth of your actions/skills.
Overall, it's a nice mix of ability scores, skills, and saving throws that are more thoughtfully integrated into a cohesive whole. But the emphasis in Blades in the Dark is not on d20 + Modifier action resolution. The emphasis is on dramatic conflict that arises from its action-based dice pool system. Attributes are present but they are not somehow imagined as the defining qualities of a character's natural talents in the way that ability scores in D&D are.