Sixteen Queens Puzzle

The sixteen queens puzzle is a variation of the eight queens puzzle. Here is a brief description of what the eight queens puzzle is: You are to arrange eight queens in a chessboard such that none is able to capture another using a single queen's move. To try it out for yourself you might want to use the pawns as queens. For a detailed information on the puzzle see: http://en.wikipedia.org/wiki/Eight_queens_puzzle

Now lets come back to the sixteen queens puzzle. What you need to do for this puzzle is pretty simple; you have to find two solutions of the eight queens puzzle in a single chess board. Bear in mind that it is not to say that none of the sixteen queens will be able to capture any other, that is impossible. Instead there are two sets of eight queens (white and black in the image) and any one queen of one set will not be able to capture another queen of the same set. Also bear in mind that if there is a queen of another set between two queens of the same set, the two queens are said to be able to capture each other, ie to say a different set is transparent to the set one is concerned with. Thus the only purpose of an addition set is to constrict the number of spaces availabe.

I did find one solution to this problem (see image) and am wondering if two is the maximum number of eight queens puzzle solution one can have in a single board? Further how many solutions are there for the sixteen queens puzzle?