If we're aiming big - though I wouldn't want to keep it as a house pet, this is more like an ultimate dream though - basically I'd purchase a massive area of land and forest in some place like India, and I'd get an old mother tiger who's still raising a cub but too old to care for it much longer, then help the cub grow up on my own, it'd be a companion and a friend but never a "pet" that I owned, and it'd be able to roam freely throughout the many miles of land surrounding, with wild game for it to hunt and fantastic landscape for it to explore - it could come and go as it pleases, though I'd hope that it would make regular appearances to see me and I could drop some LSD and sit with my lovely tiger friend and chill, I've had a "subconscious" tiger guide me through my OEVs in a lot of my 2C-E trips so it seems fitting. I could never confine such a beautiful creature to a small home and take away its freedom though - and given that tigers are often hunted in India I'd also hire a team of guards to monitor the tiger via GPS tagging and patrol the location to keep out poachers, then open it as a sanctuary for people to come for a relaxing vacation and meet the wildlife, take some powerful psychedelics among nature, and meet my tiger buddy of course :D
Alternatively a Wolf in a similar situation, where the Wolf would be free to roam a massive section of land with its pack and I'd just help it grow up (and its fellow pack members) and get friendly with them and offer them a place of shelter and food whenever they choose to visit, along with ensuring that their enclave was protected from poachers and nasties.
Or if I ever went to live on the Sea I'd go hunting for an Octopus and study it and track it across the Ocean, following its journies and watching it grow and change, learning about it from a distance, maybe swimming with it. I'm much more of a fan of animal "friends" than animal "pets"
A more realistic one though would be one of the Russian domesticated foxes, which would be more of a regular pet:
Though I already have three wonderful dogs and an adorable cat so no more pets for me any time soon
