"Many" is a subjective term. It doesn't tell you anything quantifiable, merely what the describer thinks is a larger than usual number.
For example, someone who has never owned pets might think that someone who owns 2 cats and a dog has "many" pets, while someone who does own pets might only consider that to be a "normal" number of pets.
This is actually a great point. I have zero personal interest in pets or plants, so I'm always baffled by how people can live with animals running around at home or with plants cluttering up the home. I understand the appeal to others, I just don't relate. So for me a few pets or plants is indeed already 'many'.
For example, someone who has never owned pets might think that someone who owns 2 cats and a dog has "many" pets, while someone who does own pets might only consider that to be a "normal" number of pets.