Conventional lenders will cap your residential holdings at a max of 10 mortgages. Dumb, I agree, but that's the world according to Fannie Mae and right now no one is doing anything outside of the box.
Collateralizing just means that you are pledging the collateral in one property to guarantee performance on the subject property. We do this occasionally when we make a private loan if the deal is too "thin" we will also tie up another property in the investor's portfolio to ensure performance.
And having the props "owned" by your LLC is not the same as having the financing originated and vested in the LLC. Maybe I need some clarification here...
Typically, you have a couple of options -
1) Refinance your props into a loan in the name of your LLC. You'll need 30% equity but it will come off your personal credit.
2) Refinance your props into a commercial blanket loan. This is tougher but it means you'll consolidate 10 loans into 1. They must have 25% equity and cash flow.
OR, if you are looking for a line of credit using the equity in your holdings as collateral, you'll need a good equity %. Many people think that if they are at 80% LTV, a bank will give them a LOC equal to the remaining 20% to theoretically leverage the prop to 100% - this is not the case.
For both options many of my clients are having good luck with portfolio lenders such as credit unions.