I've done pet food in my spice/dehydrated vegetable plant way back at my first QA job. It was a dried mix of some vegetables with diced apple being the only different ingredient. We had COA's from the ingredient suppliers that the ingredients were essentially human grade, and it wasn't a far enough deviation from our standard HACCP plan to need a new plan. Admittedly, as this was a third party tolling operation (we owned none of the raw ingredients and were processing/packaging on behalf of contracted customers), our HACCP plan was more focused on the equipment instead of the ingredients as a whole.
But I'm chiming in to echo the others above: you can do it so long as either your current RA fits the profile of the ingredients, or a new HACCP plan covers the process. It's been awhile since I was involved in this, but I do remember some requirements being a bit more stringent for pathogen control. This was circa 2015 for me, but after some of the pet food salmonella issues in the mid 2000's, there was quite a bit of scrutiny on ingredients at that time. We would joke that our pet food contracts had better paperwork than our spice customers because of this lol.