The highly pathogenic H5 avian flu turned up in initial tests at five more farms in Iowa, including a commercial egg operation housing up to 5.5 million birds, Iowa’s agriculture department said on Thursday.

If the virus is confirmed at the farms in additional tests underway at a federal Agriculture Department laboratory, the number of American cases could surpass 20 million birds and result in the biggest death toll in a bird flu outbreak in United States history.

The latest case, at an egg farm in Buena Vista County, could be the largest single operation to be hit in the current outbreak.

The egg farm’s owner, Rembrandt Foods, one of the top egg producers in the United States, confirmed the outbreak but disputed the number of birds affected. The state did not identify the affected farm by name.