In fact the Wazir-Dabbabah and the Ferz-Alfil have already been invented by T.R. Dawson.
To quote :
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A compound leaper is a piece that can make two or more different, non-null, patterns of leap. The simplest and best known of course is the king. Names for all combinations using coordinates less than 3 are:
{0,1} + {1,1} = king,
{0,1}+{0,2} = wazaba, {1,1}+{0,2} = diamond,
{0,1}+(1,2} = emperor, {1,1}+{1,2} = prince, {0,2}+{1,2} = templar,
{0,1}+{2,2} = caliph, {1,1}+{2,2} = ferfil, {0,2}+{2,2} = alibaba, {1,2}+{2,2} = hospitaler.
Some other combinations named by chess problemists are:
{0,2}+{1,2}+{2,2} = squirrel, {1,2}+{1,3} = gnu, {1,3}+{2,3} = bison.
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from : http://www.ktn.freeuk.com/9a.htm#(3)
On a different note :
Ralph Betza's Waffle and Chu Shogi's Phoenix are also called the Caliph. Charels Gilman's piece of the same name is a misnomer, because the Caliph is not a religious title. (It means successor.)