Helminthic therapy for pets
There has been some discussion in the Helminthic Therapy Support group about the possible use of this therapy in pets, especially cats and dogs, and there is evidence that helminth products can produce immunomodulatory effects in dogs. 
The deworming of animals can have similar adverse consequences to those seen in humans. For example it has been suggested that the routine deworming of dogs may be contributing to allergies, inflammation and autoimmune disease in these animals, in the same way that the loss of helminths has led to these conditions in humans.
The use of anthelmintic treatments in dogs has also resulted in the appearance of a multidrug-resistant strain of the canine hookworm, A. caninum,  and, in horses, the removal of adult cyathostomins has led to an altered faecal microbiota and the promotion of an inflammatory phenotype.
The following comment is from a member of the Helminthic Therapy Support group on Facebook.
Obviously, this is a topic that pet owners will want to discuss with their veterinarian/veterinary surgeon but, even when it is decided to worm a pet periodically, it is still possible for it to benefit from the immune modulation provided by therapeutic helminths. For example, dogs can be given worming medicine just before they are due to receive a fresh dose of a therapeutic helminth. This way, they and their owners will be protected against the possibility of a disease caused by pathogenic worms, but there will only be a minimal break in the benefits afforded by whichever symbiotic helminth is being used.
Best currently available species
Hymenolepis diminuta cysticercoids (HDC)
When someone asked whether H. diminuta cysticercoids (HDC) might be safe to give to a 6 week old kitten to prevent it developing allergies, etc., an expert in the use of HDC in humans suggested that this species would indeed be safe for a kitten, and pointed out that HD normally lives in insects and that cats often catch and eat insects without ill effects. HDC can be purchased from several of the helminth providers and are easy to grow at home.
Trichuris suis ova (TSO)
During toxicity studies carried out on TSO, this organisms was tested in mice, rats, rabbits, dogs and monkeys, with no problems being recorded. 
She had constant diarrhea that was not the result of parasites (we tested her poo). I tried several different types of foods and nothing was helping.
She also had something called Esonophilic Plaques. Excess esonophils were being deposited in scabby itchy spots in the skin on her back legs. (this was diagnosed by a vet btw. I initially thought it might be mange but this is a disease cats can get apparently.) She was constantly stopping and licking/biting her legs to the point where she had good sized bald spots on the backs of her legs and seemed pretty uncomfortable.
I was assured by the TSO provider that it was safe for animals and they have other customers that give it to their pets. And she definitely seemed like a good candidate. I had some dewormer on hand for her just in case but never needed it.
I had to guess with dosing. She weighed 7 lbs when I started so I gave her 0.2 ml TSO (from a bottle of 2500 ova) at the beginning of May. I mixed it in a Churu treat. I take TSO weekly myself so it was easier for me to keep her on a weekly schedule instead of bi weekly and give her a dose at the same time I took mine. She is at 0.35 ml TSO weekly now.
I’m pleased to report that her diarrhea has completely cleared up and her plaques are almost totally gone. The bald spots are gone as well. She still had one very small scabby spot I felt today but each time I check for plaques there is less and less.She is active and playful, her eyes are bright, her coat is shiny, and she has gained a pound. She also seems really happy. I’m so pleased it worked. 
Alternative species with some disadvantages
Four further species of helminth have been suggested as possibly having therapeutic value in pets, but each has disadvantages.
Necator americanus (NA)
However, caution is recommended when considering administration of NA to dogs. NA is closely related to the dog hookworm , so should feel sufficiently at home inside a dog to mature, mate and produce eggs that would be passed in the animal's feces. Infective larvae could potentially result from even a small amount of infected dog feces left on soil or grass during warmer months. These larvae could infect other animals, and even humans.
Dipylidium caninum (also called the flea tapeworm, double-pored tapeworm or cucumber tapeworm) may be suitable for dogs and cats
D. caninum can, rarely, infect human pet-owners, and especially young children.  According to Wikipedia, most infections in humans are asymptomatic, but can result in any of the following symptoms: mild diarrhea, abdominal colic, anorexia, restlessness, constipation, rectal itching, and pain due to emerging proglottids through the anal cavity. 
Trichuris vulpis may be appropriate for dogs.  However, the risk is quite high that dogs treated with TV ova will shed eggs wherever they defecate, potentially leading to unintended infection in other pets. 
Uncinaria stenocephala known in the UK as the northern hookworm, this is the most common canine hookworm in cooler regions, such as Canada and the northern parts of the US. Also known to infect cats, U. stenocephala may be a possible therapeutic species for cats and dogs,  but it can also be transmitted to humans.
Sources of mutualistic helminths
Suppliers of TSO, HDC and NA can be found on the following page.
This topic has featured in the following discussions.
- Planning to protect a new puppy’s microbiome. 
- Skin problems in dogs. Are helminths the answer? 
Also of possible interest.
- Of dogs and hookworms: man’s best friend and his parasites as a model for translational biomedical research -- Full text | PDF