To what level of detail and why ?
If you want to know ALL the reasons and variables then you have to go to university to one of the recognised automotive deisng course and in 4 years you'll knwo them ALL
There are also numerous books on race car setup and design which go through most of the basics of suspension design. BUT theses are heavy reading without a strong engineering/technical background.
The simple answer is the one given, everything which alters the tyre contact to the road and alters the polar moment of the vehcle affects the hadling. THEN add the dyanmics of weight transfer front to back AND side/side - ie corner weights AND then the compiance/rebound on the suspension and the driver input. There isnt' a simple answer. it woudl take many 10s of thousand sof words to go through each of them and lots of math to calcualte and understand it.
Sorry it's not the asnwer you're lookign for but sometimes there are no easy answers orquick shortcuts.
If you start out with a fixed car configuration the BIGGEST difference you can make is in the tyres and the camber of the wheels. But even that varies significantly between different suspension - macpherson, wishbone, anti-roll, etc etc.
Why not give soem background and we can mayeb give you more focussed information. I'm afraid we can't write the complete treatise on it in the time avaialble