There are rules related to the maximum number of financed properties you can have. These are for investment property buyers. There are some mortgage agencies, like Fannie Mae, that will not do a loan for an investment property buyer that already has what they consider to be excessive financed properties.
What if you are buying a new primary residence? Then there is no limit to the number of financed properties that you already have.
However, if you are buying a second home/vacation home or rental property there are rules. You cannot have more than 10 financed properties already.
The overall mandate for an agency like Fannie Mae is to increase homeownership, not to necessarily finance landlords who dream of having dozens of rental properties and want to finance each of them. So, they have a limit, and right now that limit is no more than 10 financed properties.
If you have 10 financed properties and are trying to buy an 11th financed investment property, you would not be able to get a Fannie Mae loan.
With 9 financed properties and if are trying to buy a 10th financed investment property, you would be able to get a Fannie Mae loan.
If you owned 85 rental properties free and clear, and are buying your first financed investment property, you would be able to get a Fannie Mae loan.
With 14 financed rental properties and if you are buying a primary residence, you would be able to get a Fannie Mae loan.