One man, Robert Gilbert Smith, 27, of no fixed address, pleaded guilty on March 20 to the charges and another two, Alan Clarke, 36, and Patrick Clarke, 32, both of Melbourne Road, Newham, London, will appear at Birmingham Crown Court on April 20 to make their pleas.
The charges relate to a string of Chinese artefacts and rhino horns targeted in seven incidents in four months in 2012 - two thefts and an attempted theft from Durham University Oriental Museum and further incidents at Gorringes auction house in Lewes, East Sussex, Norwich Castle Museum in Norfolk, the Powell Cotton Museum in Kent and the Fitzwilliam Museum in Cambridge.
Twelve of the men, aged between 25 and 67, were arrested in a series of warrants across the UK and Ireland in 2013 by police forces and the National Crime Agency.
The 13th, Daniel O'Brien, 44, of Orchard Drive, Smithy Fen, Cottenham, Cambridgeshire, was arrested in November last year and the 14th, Danny Flynn, 44, of the same address, was arrested on European arrest warrant in Dublin in January this year.
Two trial dates have been set for Birmingham Crown Court. The first on May 11 is expected to last for eight weeks and the second on September 21 is expected to last for six weeks.