But the realtor says it's "non-financeable" and explains that it won't meet Freddie Mac/Fannie Mae requirements and they will only accept cash offers.  

Talk to people, tell them you're looking to buy a house in X-neighborhood - you'd be surprised how many people know someone who heard from someone that someone is selling their deceased Aunt Mae's house.

Fannie Mae's or Freddie Mac's automated underwriting system is going to look at the full scenario, including your credit report, down payment, assets saved on top of that, income, etc etc, and call out how many years it wants. 

Fannie Mae has no limits on how many investment loans in a condo complex, they just have the below guidelines about a Single Entity owning a certain numbers/% of condos in a complex:Single-Entity OwnershipA project meets the definition of single-entity ownership when a single entity (the same individual, investor group, partnership, or corporation) owns more than the following total number of units in the project:projects with 5 to 20 units – 2 unitsprojects with 21 or more units – 20%

@Aaron KaminerYes, fannie mae /freddie mac set a limit of 10 loans. 

As the title states, do they give priority to cash offers or offers using one of their mortgage products?Thank you!

But that fell through because there's an issue with the way the original title was keyed into some system on the Fanny Mae end, and they couldn't find the exact address that's written on the title in the system and Fanny won't change it to match the title, therefore, I can't get an approval for the refinance.

My loan office just inform me that, Frannie Mae just came out with a new guideline.

Scott Campbell Fannie Mae will allow you to use 75% of the projected rental income on the property your buying, even without a history of rental income on your taxes.

If your numbers are right and you can qualify for Fannie Mae financing, then I like this deal.