DSM-Firmenich AG has invited Apollo Global Management Inc. back into the auction of its animal nutrition and health unit, creating a drawn-out two-horse race with CVC Capital Partners Plc, according to people familiar with the matter.

The sale has been hampered by differences over price and the challenging vitamins part of the business, with both buyout firms pushing DSM to separate that unit from the disposal, said the people, who asked not to be identified because discussions are private.