The gereleth and the modron do have a finite number. As I'm seeing two of a kind, I'm looking for the third race with this feature.
(Anyway I still wonder why a chaotic race like the gereleth sticks to the rule of three that much while a lawful race like the modrons use a system based on 2 instead.)
Exactly - I was wondering if a third race with a finite number is already known.
If not I'd have to take a trip around the planes and look for it. 
I think whatever the Gereleths are doing to win the Cosmic Game, it isn't a matter of mass numbers. We know they can increase their numbers, but I suspect the anti-sacred numerology (3,333 of each race) means something to and for them.
I do suspect the 'leths + Apomps have a plan for to win creation for themselves.
If you are looking to make one up, I would suggest that the third race be roughly intermediate between the two on the Ring -- the modrons are in Mechanus, the 'leths are in Carceri, and while 16 planes can't be perfectly subdivided, either the Beastlands or Arborea would be about a third of the way around from the other two. I would suggest Arborea, which puts the 'leths at the balance of the other two and suggests an ominous lack in Bytopia.
I would suggest that such a race would be angels of Greek mathematics, spirits of the Platonic shapes and solids, as well as angels of the mathematics of probability, randomness and chaos. For example, there could be 65,537 of them, the largest (known) Fermat prime, and the number of sides of the largest primitive constructible polygon. They could have powers that arise when they gather in groups of 3, 5, 17, 257, or the entire race.
Another option is to have a race with 8,128 members. This is a perfect number, which the Greeks believed had great mystical importance. Smaller perfect numbers are 6, 28, and 496. Alternatively, the 6th perfect number is 8,589,869,056 -- too large a number to ever gather together, unlike the 'leths which you might conceivably see all of, but 6 is itself perfect, so it's a kind of perfect perfect number, and the number 8,589,869,056 is equal to 2^(2^(2^2)) * (2^(2^(2^2))*2-1), the latter being prime (as Euclid predicted).
I kind of like the perfect number option, since the geometry angle gets people thinking of dice and modrons. For powers, I would suggest tricks like the Fatespinner prestige class (modifying dice rolls), mirror image and similar spells (they double themselves) any dimension (*) spell for the higher-level members, or prediction abilities like divination (or foresight for real bloods of the race).
Some of them should have elemental themes; the Greek associated numbers as well as shapes with elements. Actually, modrons seem to care about the Outer Planes and 'leths seem to focus on the Prime. Perhaps this number-angel race should focus on the Inner Planes, with their 6 major planes and the many combinations of them that can be found. They could be sustained by a general belief in the perfection and infinite possibility of the material universe. As for their form, they might basically look like elementals! Except that they tend to glow, and are probably much chattier. For a more distinct form, they could look like floating magic circles filled with numbers and geometric diagrams, made out of water, fire, stone, lightning, or pos/neg energy.
Thanks for the input, I'll do some research on those ideas you gave.
There is a rumor that only one adamantite dragon exists.
As to the modrons sticking to base 2 (i.e. binary); it is the most logical of systems. A value is one thing or another. There is no middle ground or ambiguity
As to the tertiary system of the gehreleths, I don't believe there was an official explanation. I think they left it with there being some sinister implication/grand plan behind their design and the rules involved (and it piqued my interest in them and had me trying to work out theories as to the "why" of it - not that I came up with anything very good)
Based on your title, are you angling for a third race with a finite number based around some numeric system?