Portfolio lenders are tough to find, but they are out there so keep looking. Look at credit unions and local banks (2-5 branches). You say each property is profitable, put them through the BP calculator and print them; now you have actual number to show a lender that they are profitable. Also create a balance sheet that shows property value, loan amount, int rate, total payment,principle payment, int payment, insurance payment, and LTV (let me know if you want an example). A lender can look at the balance sheet and make a quick decision, then dig into each property if they want. Also have past two years of taxes and be ready to provide two months bank statements of business and personal checking accounts.
If you can't find a local portfolio lender, there are some national lenders that will lend on 5 or more properties. But, these are commercial loans; higher int rate, lower LTV ratios. Check out RCN Capital.
Let me know if you have any questions. Good luck.