可以。但一般不能再读相同专业的博士学位。比如，加州大学伯克利分校就有这么一条规定：

Duplication of Doctoral DegreeStudents who already hold a doctoral level degree are not admitted and duplication of degree or admission to a lesser degree is not permitted. However, in extraordinary circumstances, the faculty of the department may request an exception from the Dean of the Graduate Division. The department must demonstrate that the second degree field of study and program are distinctly different from that of the original degree, and that there is a professional or scholarly purpose that requires this second degree.

简译如下：

“已经拥有博士学位的学生，原则上是不允许再申请PhD或比PhD更低阶的学位项目的。但特殊情况下，应教师或学系的申请，研究生部可能会网开一面。（向研究部）提出这种申请时，学系必须提供足够的证据证明，这位学生即将攻读的专业领域与之前是截然不同的，而且是非常有必要再读一个学位的。”

就是说同一专业领域已经拥有博士学位再来加州大学伯克利分校读博士学位是没有意义的。但如果不是同一领域的话，是可以的。这种案例每年都有很多。比如国内博士是物理，去美国读经济学、数学或者计算机科学博士都可以。