He also played in Lanús of Argentina, Santos Laguna, Atlas, Cruz Azul, Leon, and Irapuato of Mexico.
Caniza was a regular in the Paraguay national football team because of his versatility, as he can play as a side defender or as a centre-back.
However, when coach Gerardo Martino took the helm of the national team Caniza was called back and accepted to return to play for Paraguay.
Caniza holds the distinction as the only Paraguayan footballer to be selected for 4 consecutive FIFA World Cup Finals, having been chosen in 1998, 2002, 2006 and 2010.
Due to his small size and industrial play, he has been described by BBC South American reporter Tim Vickery as "the Paraguayan Nobby Stiles".