Actually what I prefer is if my place of work would just give me benefit dollars that I could use as I wish. Like for a petsitter, dog vet visits. That would be really great. After all they are not having to pay for anyone else on my health insurance,etc. I'm a bargain so to speak. Will it happen? Well maybe after pigs start flying.
It was a little easier for us because we were in the business that allowed us to use Maggie (and our other dog Abbey for years) Guiding backpacking/flyfishing/hunting trips. We also have a great tax guy that uses his dogs in various ways as write-offs. (Too confusing for me)
They still are more expensive in the long run! Dog food, supplies, vet bills, etc. But well worth it.
I think it would only work if you had to show proof of vet visits, etc. Maybe write off rabies shots (since they are mandatory) and if you had a life saving surgery done ... just routine care would get way out of control.
You can write off foster care as a tax deduction, if any one is thinking about it! ;D As long as the rescue group you are doing foster care for is 401(3)(c).