I totally do not understand tiered care. I can understand having a limit on what you will spend on any pet due to finances but to say one pet's life is worth more than another makes no sense to me at all.
This is why Congress needs to put me on the death panels for public healthcare. I will have an opinion and can make decisions about these things.
Now, less facetiously I will give an overview of my approach to pet care here although I fully expect that is won't "make sense" to you, and that is ok:
I have 4 dogs, 1 of which I actively sought as a pet. No, I didn't "buy" her, she was given to me by people I've known for 20 years in this breed. She goes to the expensive vet who I believe is better than our garden variety vet; she also went to the board certified surgeon rather than to her own vet for specialized surgery.
I feel a higher kind of obligation toward her since I got her as a fairly young dog (4 years old) and there were MANY homes she could have gone to. This is a breed (French bulldog) that is uber hot right now, unfortunately. ugh I hate that, but that's another issue.
The other 3 dogs were more of a "rescue" situation. Our big boy was dumped into rescue due to severe health problems. I adopted him, not to "save" him, but because he's a fabulous dog and he's a great fit in our house. He puts up with the bossy Frenchies. Frankly, it would have been hard to place him elsewhere, anyway. His medication costs $1300 annually and a few days ago he had emergency surgery for kidney stones, $2,000 in surgery, I know that he needs another $$$ in entropian surgery. And there is something bad going on with his gums. I'm not sure how much more I will spend on health care for this dog and just as important, I don't know how much more medical care and time away form work I can take for him. His immune system and general overall health is compromised yet he feels great and is happy at the moment, so we will take it day by day. He isn't a candidate for heroic measures. But I already love him more than all of the others combined, I am besotted with him. But I will listen to the little voice inside that says: enough! enough for him, enough for me.
Our 2 remaining Frenchie girls are elderly. They were in a semi-rescue situation and they "had to be placed together." No one is gonna take two elderly dogs. I took them thinking "how long can they live, anyway?" 3 years later, they are still going strong. So, they go to our general vet but they will not have surgery, ever. They are a risk for anesthesia and I won't let the general vet do that. Nor will I pay for a higher end vet. Palliative care is the watchword for these two girls.
One of our elderly girls is a biter. If and when her eyes become compromised, as are the eyes of the others here, I may euthanize her. The idea of fighting with her twice daily for eye meds is depressing to me. Both DH and I have multiple bites form this dog already. That's not a life for either of us.
Which brings me to cats. I will not fight with a cat daily for medication. Dogs, OTOH are easy to pill, just wrap it in cheese.
My tiered approach is a combination of age of pet, ease of caring for them, general overall health and likelihood of complete success in treatment, and my initial obligation in adoption.