我和曹老师在比较从句方面理解不同，大家共同探讨。我是这样理解的：

He dances better than sings.

网友的句式没有问题，但better改用more 更准确。这属于自己和自己比较，为避免重复，主语自然省略,这种句型一般是实义动词不带宾语。按照《牛津用法指南》作者Swan的解释，than类似关系代词，从句主语可以省略。请看外刊类似例句：

1.They can write better than speak and should be encouraged to do so.

2. Fund-raising is a long-term boost at best, but most institutions cannot do better than run in place.

3. I promise you they'll do more than cry.

（以上几个例句均为实义动词不带宾语）

我觉得一本语法书不可能包罗万象，有些变化可能被忽略了，因为例句的数量有限，又受篇幅限制，而且读者的思考角度也会不同，作者难以想的面面俱到。《剑桥语法》也有自己的短板。比如《剑桥语法》的例句：

[iv] The difficulties are even greater than appears at first sight.

该书认为这个句子than 部分可以补全还原为：

...than it appears at first sight that the difficulties are great.

这个解释没有错，但是这里作者疏忽了另一种情况，即appear 可以用复数。如果用复数，应该是相同比较对象的省略。显然就不能理解为 it appears that... 了, 因为形式主语it 只能是单数，我觉得这可能是该书作者没有写上的一个变化。这样可能使有些读者，如我们的一些网友，会误以为这里的appear 不能用复数。其实appear 用复数的情形也很普遍。例如：

The differences are more profound than appear at first sight.

此句应该补全还原为：

The differences are more profound than (they) appear at first sight.

they指differences.

类似例句很多，我仅提供几个国外出版物上的为例如下：

1. That Fisher's poetry is full of forms does not imply that there are more things in its heaven and earth than appear at first sight. (Angela Leiton: On Form: Poetry, Aestheticism, and the Legacy of a Word, 2008年版 p.236)

2. In fact , as Miller pointed out in 1895 , there are more similarities between the two maps than appear at first sight. (Michael Prestwich: Thirteenth Century England VIII, 2001版 p175)

3. The differences are more profound than appear at first sight. (Lucien Girardier: Mammalian Thermogenesis, 2012年版p 4)

4. The shifts required were much larger than appear at first sight, and all the harder to make.

当然appear复数，和网友问题关系不大，我仅是用这个例子来证明该语法书的局限性。