One object can have multiple gradients as seen in the image 1 (below).
To add multiple gradients, open your appearances panel and duplicate the fill. Note that the second gradient has to have a blending mode or transparency for this to work.

Image 1: Two radial gradients in same object.
Answer from joojaa on Stack ExchangeOne object can have multiple gradients as seen in the image 1 (below).
To add multiple gradients, open your appearances panel and duplicate the fill. Note that the second gradient has to have a blending mode or transparency for this to work.

Image 1: Two radial gradients in same object.
You can add multiple gradient fills to an object via the Appearance panel.
If you need more complex gradients you can use the Mesh Tool to create a gradient mesh. Simply click on a point with the Mesh Tool to create a mesh from the object, you can then change the color of each individual point.
A simply rectangle with each corner point set to a different color:

For more complex gradients just keep adding points:

You can expand an existing gradient fill to a gradient mesh by selecting the object, expanding (Object → Expand) and selecting "Gradient Mesh":

- Create and edit mesh objects in Illustrator - Adobe Support
The best recommendation would be to add multiple fills to the object and then make one the base fill and one the overlay. The base fill would have normal transparency settings and the second fill could do the extra highlights. This would allow you to set the opacity and blending mode for the top gradient. This means your object is still solid and has a default transparency and blending mode, but one of the fills won't. Much more control this way.
For a start: you don't have to duplicate the object. You can add multiple fills to the same object in the appearance palette. However I'm not sure about which transparency settings would be right.
Does anyone know if you can make multiple linear gradients on the same path on Adobe illustrator for the iPad. I little experience and no formal training with the program. For example, can I add another gradient line with the same colors that would replace the red line on this screenshot?
Help applying shading gradient across group/layers/multiple shapes
How to blend two gradients?
How do I apply a gradient across multiple objects in Illustrator? - Graphic Design Stack Exchange
SOLVED!
Second and preferred solution given by u/AnAvailableHandle in thread
First solution given by: u/SavageAnimator"Select all objects and group them. Duplicate the group. Smash 'em into one single shape with the Pathfinder to create a new shape that is the exact size of the thing you're making. Place the new shape above the original group in the layer stack. Select the group and the top shape. Ctrl/Cmd+7 to make a new group with the top shape as a mask for the rest of the group. Add effects and place them in the masked group to have them masked out properly."
while the first solution gives me identical effects, the second solution ended up being more modular
I'm pretty well versed in photoshop, but decided to start learning how to use illustrator to get a better grasp and control of vectors. But, my hair is falling out from trying for a couple of hours trying to figure this one out.
I KNOW there must be an easier way to do this, and would love some help on how to apply a shading gradient over a group or selection of shapes/layers
Here's what I've tried so far
here's the original group/layers shape
I tried making a compound path with all layers/group, but it isn't working the way i want it to
I tried selecting all the layers/group but it's only making a gradient over one layer.
I tried copying the largest object to a new layer, then putting it over the group, and then applying a shading gradient but it's missing some of the parts of the other layers/group
Anyone know how to blend two separate gradients?
Best luck I have had so far is adding a third object with a gradient...its very close but not seamless.
Any other ideas?
Thanks!
In order to get a single gradient to cover multiple objects, you need to use the Gradient Tool.

Select your objects, then with the Gradient Tool, click and drag from where you want the gradient to start, and let go where you want the gradient to end.

This will cause the gradient to cover all selected objects. You can then modify gradient settings using the Gradient Panel
Alternatively you can create a Compound Shape of the multiple objects, if feasible, and that will allow a gradient to see the compound shape as one object. However, Compound Shapes are not always a good solution for overall construction. It depends upon the artwork.
From http://www.bittbox.com/illustrator/illustrator-101-one-gradient-across-multiple-paths:
Select all of the objects you want to include
Object menu > Compound Object > Make (Cmd+8, Ctrl+8)
Apply your gradient to the gradient path.