Blended rates for 2 combined mortgages?

[Ismael Ayala Jr.]

I currently have a rental property that has >$100,000, maybe $130,000 of equity. Would a bank(say like BankofAmer) allow me to assume the low interest rate of another property and blend the interest rate with my current rental property? Based on my equity, creditworthiness, and history with them? I already do business with BankofAmer. But if not BankofAmer, would another mortgage lender take on the 2 mortgages and blend the interest rates together based on my credit and possibly even cash flow? Thx.