Can I Pass Additional Parameter To An Event?

Not to "event", but to an event handler.

Parameters of the even handlers are defined by the "event arguments" class (derived from System.EventArgs); and you cannot change the signature of the event handler. So, you should have asked, "can I pass additional information?". Of course you can.

(If it was the event you define yourself, you would need to create you own event arguments class where you would put all the information you need. In your case of Paint event, this is not an option.)

You can implement rendering on one of two ways: 1) overriding Control.OnPaint; 2) handling the event .Control.Paint. The signatures of these methods are:

protected override void OnPaint(PaintEventArgs e) { /* ... */ }

//...

// alternatively, an event handler:
void SomeEventHandlerOfThePaintEvent(object sender, PaintEventArgs e) { /* ... */ }

How many parameters are there? The answer 1 and 2 would be wrong. Actually, it's 2 and 3. There is one more hidden argument: "this", because first method is the instance (non-static) method; and any event handler can be instance one. You can use "this" to pass any additional information (and this is the very basic element of the beginners of OOP, not even using the heart of OOP: late binding):

using System.Windows.Forms;
using System.Drawing;
//...

class SomeControl : Control {

    Color someGradientColor;
    Color CalculteAnotherGradientColor() { /* ... */ }

    protected override void OnPaint(PaintEventArgs e) {
        // use someGradientColor here
        // ...
        Color someColorToRender = CalculteAnotherGradientColor();
        // and so on...
        // for further detail, please see my past answers referenced below
    }

} //class SomeControl

Something like that.

Please see also my past answers:

Static vs instance methods:
Type casting in c#[^],
C# windows base this key word related and its uses in the application[^],
What makes static methods accessible?[^];
Rendering graphics with passing data:
What kind of playful method is Paint? (DataGridViewImageCell.Paint(...))[^],
capture the drawing on a panel[^],
Drawing Lines between mdi child forms[^],
How to speed up my vb.net application?[^],
Zoom image in C# .net mouse wheel[^].

—SA