Summary
The Symbology interface in ArcMap is great for applying multiple symbols to different values. However, it is a bit less obvious when you want to apply a change to multiple different symbols without changing the unique colors. For example, applying an offset shadow to many lines with different colors, as shown in the images below.
Before:

After:

Procedure
To apply shadows in batch to lines with different colors using Unique Values symbology, use the following steps:
- Bring the feature class into ArcMap.
- Double-click on the layer in the Table of Contents.
- Click Categories > Unique values and choose the desired Value Field.

- Click Add All Values and uncheck <all other values>.

- Click Symbol at the top left of the values list > Properties for All Symbols.

- Click Edit Symbol on the right.

- At the top of the Symbol Property Editor, choose Type: Cartographic Line Symbol.

- Set the width as desired.

- On the left-hand side, under Layers, click + to add a new layer and increase the width to match the other line.

- Click the down arrow under the Layers section on the left to be sure the second line is at the bottom of the list of symbol layers.

- Go to the Line Properties tab and increase or decrease the offset - this creates the shadow. Click OK twice.

- Apply unique colors to the lines by clicking the Color Ramp drop-down above the top right of the value table. Choose a ramp with separated color blocks with a variety of colors.

This applies shadows to multiple different colored lines. If you need to change each individual line color, double-click the line and change the color using the palette to the right, and click OK.