A friend is an animal rescuer, with hundreds of cats, dogs, and more. Decades of experience, 4 veterinarians on staff. One of his cats was dying, and would not eat.
Now... our Tigger is near and dear to our hearts and we have tested a variety of foods in A/B testing. Very discriminating, as a large part of his diet is rodents, a bare minimum of 200 rats/voles/mice/moles/goghers per year, plus rabbits and squirrels and some birds.
Tigger is adamant that this is the best damned stuff short of fresh warm rabbit brains:
You can try other flavors and maybe your cat will like those better, but Tigger has made his preferences very clear. Nor does he like the dry patties style.
“Meow meow meow rabbit nibs” — Tigger
Back to that dying cat: it loved this food and it extended its life and eased its suffering (died of liver cancer).
If you love your cat(s) as we do, this is the food. It is a premium ($$$) product, and so being so expensive Tigger gets another cheaper but still good quality food for breakfast, the good stuff he gets for dinner.
We don’t have a dog (Tigger has vetoed the idea so far), but food quality matters to every animal (especially people!). Dogs might benefit from Vital Essentials dog food @AMAZON.
Getting more calories into your cat
Duck fat has nutrients and is high calorie and Tigger gives it two claws up.
Other tips for cat calories: heavy cream, unsalted butter, whole milk, ideally with 6% milkfat. Tigger loves all of these, and will self regulate on the duck fat and butter, so overfeeding is not an issue.
Don’t slow-poison your cat!
Feeding a cat anything but animal food means degrading its health and longevity.
Cats are obligate carnivores. Any cat food with grains is abuse of your cat (intended or not, but now you know better). And even if animal-based, a lot of foods are nasty stuff that won’t do your pet any favors on health.
Obligate or "true" carnivores are those whose diet requires nutrients found only in animal flesh. While obligate carnivores might be able to ingest small amounts of plant matter, they lack the necessary physiology required to fully digest it. Some obligate carnivorous mammals will ingest vegetation as an emetic, to self-induce vomiting the food that upset its stomach.
Obligate carnivores are diverse. The amphibian axolotl consumes mainly worms and larvae in its environment, but if necessary will consume algae.
All felids, including the domestic cat, require a diet of primarily animal flesh and organs. Specifically, cats have high protein requirements and their metabolisms appear unable to synthesize essential nutrients such as retinol, arginine, taurine, and arachidonic acid; thus, in nature, they must consume flesh to supply these nutrients.