My research indicates that you can own as many cats as you want to in the state of Michigan, USA, but you will have to comply with the state’s animal welfare laws which insist that a pet owner does not cause suffering to their cats through neglect. So although there is no specific state law which limits the number of cats that a person can own, there is an overarching law which indirectly limits the number if they are incapable of looking after them to a sufficiently high standard in compliance with the law.
Although unlikely, it is conceivable that there are cities or local authorities in Michigan where they have enacted animal welfare laws limiting cat numbers. There is little point in researching this in general. If you live within a local authority’s jurisdiction a phone call to their offices on cat ownership may be prudent. Also this post is valid as at its date. Laws change.
Animal welfare in general
Every state in America has animal welfare laws which criminalises unnecessary animal suffering through neglect or direct abuse. It appears that the law in Michigan is very similar to the laws of most countries with respect to cat ownership. At present, it is quite rare for a city or state to limit the number of cats a person can own. One day things will change, no doubt, as the human population grows. Large numbers of cats in a home is linked to cat hoarding which is a mental health condition because cat hoarders are hoarders in general. They hoard anything and are often incapable of looking after their acquired cats and blind to the neglect and suffering that they cause. These people will be limited as to cat ownership and maybe banned from owning cats at all if they’re convicted of animal abuse or cruelty.