You can modify Illustrator graphic styles via the Illustrator appearance panel (access the appearance panel via the window menu)
You will then see all the different elements such as multiple fills and multiple strokes. Modify those parts of the Illustrator graphic styles.
You can then remove the fills / strokes / effects and 'create' a new style or you can tweak the stops or color settings or add transparency to a particular element or add an effect into the mix
Original style, this Illustrator graphic style can be found in the radial styles set
A subtle change of the blending mode to modify the Illustrator graphic style - from color burn to darken for one of the fills
In this example, the gradient for one of the fill has been changed - the Illustrator graphic style is now quite different from the original
The fill has been modified by adding a new fill with a different blending mode
By repeat additions of fills and changes of the graphic styles' appearance, the style now looks like the original Illustrator graphic style.