My original question (probably poorly worded) came from the understanding that you cannot change total weight transfer from roll stiffness as it depends on centre of mass height (relative to roll centre), track width, weight, and lateral acceleration. But you can certainly tune weight transfer and hence grip from to rear with relative roll stiffness. So what happens to total grip if you stiffen (or soften) front and rear together equally... i guess nothing!
Nope, not nothing, total grip increases.
The grippiest theoretical suspension is completely solid, including the tyres (imagine magic solid tyres with no air, just a band of grippy rubber that also happens to not be able to compress at all), allowing no roll. This would give zero weight transfer and allow the tyres to reach their full potential. The downside is that you would have to have a perfectly smooth and level track to run this car on.
Forget about CoM height, roll centre height, track width, etc. Just know that making a car's suspension softer will make it tend to roll more. The mechanics needn't be any more complex than that.
Total grip is the amount of grip available when the car is in steady state, so should be regarded as 'total potential grip' rather than total grip being used at any one time, and is whatever the tyres are capable of with perfect suspension and zero weight transfer.
Lets now put a car into a corner and let it take a set. The outside suspension will compress as the car rolls and more of the car's weight will be pressing those tyres into the ground than the inside tyres. (remember the car's weight is constant, and if the suspension compresses more on the outside tyres then it must be less on the inside tyres)
The outside tyres will be working harder than normal and be able to give more grip, but the inside tyres with less weight on them lose more grip than the outside tyres gain. Ergo the softer the car, the more weight transfer and the less total grip.
Try this on for size and let us know how you get on.
https://youtu.be/qCE54-H2zkM
In particular, from about 3:20, he uses an illustration where at zero weight transfer due to steady state driving, the car has 100 'grip units'. During periods of weight transfer, the car has only 90 total grip units (explained in the video). This is why the more weight transfer you have, the less total grip you have, and why softer cars have more weight transfer and less total grip available and harder cars have more total grip available, basically due to being able to make the inside tyres work harder.