Most schools don't like duplicate degrees, especially ones in the United State. Schools in Africa or the UK usually allow it.

[I know a Professor that had 5 doctorates (not honorary doctorates).][1]

> Professor Blight (PrEng) was an A-Rated researcher who held five doctoral degrees, and who was considered as one of the world’s leading thinkers in Geotechnical Engineering. He held BSc(Eng) and MSc(Eng) qualifications from Wits. He completed his PhD in Soil Mechanics and his DSc(Eng) in Geotechnical Engineering at London University, before returning to Wits. In 1985, he obtained his DSc(Eng) in Materials Engineering from Wits and another DSc(Eng) qualification from the University of Cape Town. In 2001, he obtained a D.Eng, degree from Wits focusing on the Application of Research in Practice.
 
> With over 330 papers published in accredited journals, Professor Blight was internationally renowned as a researcher of the highest standing around the world. He was well published internationally and the author or co-author of several books.


  [1]: http://www.wits.ac.za/newsroom/newsitems/201312/22012/news_item_22012.html