Non recourse loans available to purchase multi property portfolio

[Adrian Stamer]

Hello

Up to this point I've used local small banks for commercial loans. These are always recourse. I am also aware of Fannie Mae and Freddie Mac loans which have favorable terms including being non recourse but according to my mortgage broker these wouldn't really work in this situation. The largest properties are only ~20 units at about a million in value. Portfolio is $10mil plus, any good ideas for non recourse financing?

Could split up the larger and smaller stuff but the larger properties still seem beneath Fannie Mae level individually. Looking for comparable small bank rates. 

Insurance company money a relevant product here?