可以。但一般不能再讀相同專業(yè)的博士學位。比如，加州大學伯克利分校就有這么一條規(guī)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.

簡譯如下：

“已經擁有博士學位的學生，原則上是不允許再申請PhD或比PhD更低階的學位項目的。但特殊情況下，應教師或學系的申請，研究生部可能會網開一面。（向研究部）提出這種申請時，學系必須提供足夠的證據證明，這位學生即將攻讀的專業(yè)領域與之前是截然不同的，而且是非常有必要再讀一個學位的?！?/p>

就是說同一專業(yè)領域已經擁有博士學位再來加州大學伯克利分校讀博士學位是沒有意義的。但如果不是同一領域的話，是可以的。這種案例每年都有很多。比如國內博士是物理，去美國讀經濟學、數學或者計算機科學博士都可以。