Storyboards can be keyed and run from multiple triggers, and it works great as long as it's set up properly. If I am understanding you correctly, you're hoping to apply the storyboard to each individual ListBoxItem. In which case, why not make a style, and on that style's triggers, fire the storyboard.
Excuse my pseudocode.
<Storyboard x:Key="MyEnterStoryboard">
<!-- Do Enter Work -->
</Storyboard>
<Storyboard x:Key="MyExitStoryboard">
<!-- Do Exit Work -->
</Storyboard>
<Style TargetType="{x:Type ListBoxItem}">
<Style.Triggers>
<Trigger Property="SelectedItemChanging" Value="True">
<Trigger.EnterActions>
<BeginStoryboard Storyboard="{StaticResource MyEnterStoryboard}"/>
</Trigger.EnterActions>
<Trigger.ExitActions>
<BeginStoryboard Storyboard="{StaticResource MyExitStoryboard}"/>
</Trigger.ExitActions>
</Trigger>
</Style.Triggers>
</Style>