Even slight changes to the statistics from the human baseline creates some incredibly interesting cultural assumptions.
As an easy example, let's create an uplifted Ape's genetic profile, but keep it close to the human baseline, humans are a type of ape, after all. Let's adjust Str by +1D and Soc by -1D and change Dex to Agi to see how these things change what it means to be sapient
Ape: SAEIDS (compare: Humaniti-SDEIDS) with D of 322221 for each stat.
Clearly they're stronger than humans with a 6+2D roll for Str (a chimp, even only topping 4' can rip the arms off of human quite easily), the average ape uplift is as strong as the strongest humans (Ape str goes from 7-18, with the average at 13, or D).
Instead of Dexterity for Hand-Eye coordination, they have Agility, which gives them Whole Body coordination - their sense of propioception doesn't accumulate in the hands, but extends equally throughout the body. Careers that care about it call for C2 as a Controlling Characteristic and don't call out Dex (rendering checks on Agi as Agi/2), so clearly either there are adaptive control schemes available or apes really are as good with every inch of their bodies as humans are with their hands. The Merchant career's requirement of "To begin Spacehand: Dex" means you're not going to see many ape-uplifts on Merchantmen. Perhaps this has something to do with their Soc...
The Soc dice of 1 gives them a maximum Social stat of 6.
This could mean a couple of things - one, instead of going their own way, they wish to work within 'the system' (geneering, perhaps?), but are limited in their ability to do so. Maybe they have trouble with human social cues, which can be quite subtle, or are subject to discrimination outright. Or it could simply mean that they naturally form smaller, but stable (otherwise Charisma would be the stat), groupings than humaniti does: topping out at 25, say, as opposed to humaniti's 50 or so. Either one alone or both together are just as good and interesting.
Here's a more difficult example: The uplifted Octopode.
The genetic stats could easily be SGVIIC with dice of 122232. This is very different. Their stats are Str, Grace, Vigor, Int, Instinct, Charisma.
They're not nearly as strong as humans, averaging 3.5, while humans easily double that, but they have no bony structure to provide for leverage in assisting every-day tasks in a human dominated culture. They might easily be stronger than humans, but Str 1D shows how difficult it is to operate as a non-skeletal being in a skeletal world.
They have Grace, instead of Dex, meaning their control over their limbs is phenomenal. Considering that they have between 8 and 10 depending on the species, this is probably a good thing.
Vigor indicates that their stamina is just not as good as that of humans, the Octopodes excel at short term tasks, but longer-term planning is cut short due to the limited time per day that they are active.
Instead of Education, Octopodes have Instinct, and 3D at that, giving them 6+2D in it. Their lineage doesn't include much parenting, and they learn everything as they go and by genetic memory. However, they're GOOD at it, able to almost compete with humans at their institutions of higher learning. The average Instinct for an Octopode is 13, and that reduces down to a 4, quite below the human's Educational stat. Humans don't want to breed a superior being, and the troubles that Octopodes occasionally encounter with educational systems helps keep humaniti feeling better about themselves. Fortunately, most educational institutions allow the use of native Int to pass courses, which the Octopi are easily the equal of humaniti in.
Octopodes use Charisma instead of Social Class, they don't have a species history of congregating or self-organising (except for mating, but that's not quite the same), so the most eloquent or simply the loudest of a group usually gets the others to go along. Long term social creations are a new thing to these newly fully-sapient beings, and they're still having trouble adapting to the human's world.