Suppose I have a <div>:

<li class="menu-item"> ... </li>

Could somebody tell me if I can use li.menu-item.menu-item.menu-item { ... } to make this css rule has a higher priority?

Update:

Here is the codes to illustrate this:

<ul>
    <li class="menu-item dark">Item 1</li>
    <li class="menu-item dark">Item 2</li>
    <li class="menu-item dark menu-item-special">Item 3</li>
    <li class="menu-item dark">Item 4</li>
</ul>

.menu-item.dark {
    background: #333;
    height: 40px;
    line-height: 40px;
    margin-bottom: 10px;
}
.menu-item-special.menu-item-special.menu-item-special {
    background: blue;
}

There is also a jsfiddle: http://jsfiddle.net/wenjiehu/6hycnscy/

You can see that the background colour of "Item 3" is blue.

This isn't good practice because you have to go to the spec to confirm it, but interestingly enough, it will have an effect.

Oddly enough repeating a class on a CSS declaration will boost its specificity!

I didn't believe it, but if you consult the CSS spec, there is nothing that precludes repeating a class to increase specificity:

• count 1 if the declaration is from is a 'style' attribute rather than a rule with a selector, 0 otherwise (= a) (In HTML, values of an element's "style" attribute are style sheet rules. These rules have no selectors, so a=1, b=0, c=0, and d=0.)
• count the number of ID attributes in the selector (= b)
• count the number of other attributes and pseudo-classes in the selector (= c)
• count the number of element names and pseudo-elements in the selector (= d)

So in your example:

.menu-item.dark {} 
/* a=0 b=0 c=2 d=0 -> specificity = 0,0,2,0 */
li.menu-item-special.menu-item-special.menu-item-special
/* a=0 b=0 c=3 d=0 -> specificity = 0,0,3,1 */

So that latter actually wins!

To add more context, specificity rules are hierarchical, so below #foo beats your rule, as does !important:

#foo
/* a=1 b=0 c=0 d=0 -> specificity = 0,1,0,0 */
li.menu-item-special.menu-item-special.menu-item-special
/* a=0 b=0 c=3 d=0 -> specificity = 0,0,3,1 */

Note: I've only tested this on Chrome and IE8. Because of its undefined nature some browsers may act differently.