How can I use equity across 11 res units without refinancing each

[Emmanuel N Okafor]

I have hit a brick wall in my real estate investment business. I have maxed out on rentals I can finance. I currently have 11 rentals. One is fully paid off and I just moved into a new primary house with my family. I have been buying at least one house per year for the last 6 years. I have a little over a million dollars in equity in my 11 rentals. I don't know how to leverage that equity without refinancing each house and I don't want to do that. I refinanced most of the houses last year with low interest rates. I want to wait at least 5 years before messing with the current financing so I can recover the cost of refinancing. -

I have excellent credit and a regular job with steady income. I am interested in getting into multi-family houses or apartments using a portion of my current equity. I have called many banks and no one will give me a blanket loan with my rentals as collaterals or a line of credit for the million dollars I have in equity across my 11 properties. Most commercial banks wouldn't mess with residential properties and the personal bank side wouldn't allow me to combine the equities of all my rentals. Most are offering cash-out refinancing of all the properties individually which I don't want to do 

Are there another options I should consider?