Consider a 15 year loan.

By using HELOC funds instead, or even a zero-percent credit card advance with a 4% transaction fee, they are effectively using the CREDITOR's resources instead of their own money to accelerate mortgage loan payoff (at a "cost" of a few hundred dollars per year).

If you have extra cash, payoff the initial mortgage without adding more loans.

How we purchased our property: Combination of Savings, Personal Loan with interest from a family member (4% interest) and a cash loan from Wells at about 8%.

If your partner does a conventional loan, you would sign allowing the mortgage to be recorded, but you do not need to sign as personal guarantee on the NOTE for a conventional loan either!

Whether the lender decides to do anything, and exactly what they decide to do depends on the lenders particular strategy, target ROI, risk tolerance, current interest rates, interest rate of subject mortgage loan, etc. 

I am a licensed realtor based in Atlanta, Georgia, and I am currently working on obtaining my mortgage origination license.

They hold title, and the mortgage and promissory note were attorney drafted and filed at our local county. 

Quote from @Nicholas Dillon: I read somewhere that you can request to have your mortgage insurance dropped once your Loan to Value reaches 80%.

Your loan would be on a different property so no financing on the property you are buying.