This word is acceptable for play in the US & UK dictionaries that are being used in the following games:

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v. To make mongrel in race, nature, or character.

v. To breed a mongrel

v. To cross-breed

v. To cause to be mongrel; to cross breeds, so as to produce mongrels.

To make mongrel; give a mongrel nature or character to.

v. cause to become a mongrel

"In the South, Democrats who understood nothing about the candidate as a man, nothing at all, castigated him as a symbol of “Black Republicanism”–a “sooty and scoundrelly” abolitionist who wanted to free the slaves and mongrelize the white race."

mongrelized    mongrelizing   

breed