Same Soup, Different Stir
This is me:
45 kg of oxygen, 13 kg of carbon, 7 kg of hydrogen, 2 kg of nitrogen, 1.5 kg of calcium, 0.8 kg of phosphorus, and so on.
Actually, this atom soup could be any person under 70 kg who ever lived. Take a smaller scoop and it could be my dog, the mushrooms I ate today, an octopus, a crab, or a cactus. Take a bigger one and it could be a giraffe or a sequoia.
All living organisms share basically the same recipe. The atom disposition is the only thing that sets them apart.
So if you want to be a different animal, no need to wait for reincarnation. Just rearrange yourself.