Yes, you can have up to 10 financed properties with Fannie Mae. If you know how to structure things, you can keep financing more and more purchases with Fannie Mae even after you have 10 financed properties.
"If you know how to structure things...." is kind of the question thats really being asked.
After 10 mortgaged properties, you go to Portfolio loans, those held in house and not sold to Fannie/Freddie.
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