What type of Mortgage company is the type that rents out houses to people if there exists one?

Basically I am curious if there is a mortgage company that buys houses or builds homes and rents them out to the public, I know people do this to make money like my dad does but I also know their is a limit on the amount of houses you can have per person.

Is there a way to get rid of that limit or is their a company that exists that might work like this, and if there isn't then would this be a good idea to start up a company.

Also I don't mean rent to own.

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