He is the nearest we have to an Amearican Shakespeare.

=He is the nearest to an American Shakespeare that we have 

参考译文：他几乎差不多就是我们美国的莎士比亚。

(1)the nearest to 几乎差不多就是

(2)that we have 为定语从句,关系代词that在定语从句作have的宾语。

be the nearest to (与…)最相似的;(和…)几乎差不多的（英文解释:You describe the thing most similar to something as the nearest thing to it when there is no example of the thing itself.)

It would appear that the legal profession is the nearest thing to a recession-proof industry. 

司法行业看来是最不易受经济萧条影响的领域了。

He is the nearest to a dead cert that Britain has in Albertville.  

他是英国在阿尔贝维尔冬奥会上最有希望夺取金牌的选手。