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>