Run the numbers in advance.
Understand what are the current rates for an additional 2nd mortgage, what are the rates for a brand new mortgage that will cover the additional funds. Understand what they are for another lender.
Estimate the amount of paperwork involved in each option (new first, new 2nd, and new lender).
Ask the what are the options they can offer you. Because you have estimated the costs in money and time for the different options, you can evaluate the offer they make.
What they offer you can range from everything you want to nothing you would accept. What they offer will depend on several factors: Do they care to keep you as a customer?; Do they expect you to walk away?; are they trying to get rid of mortgages like the one you have?; Can they make more money with the plan they are offering you?
You will be interested in the upfront costs, the monthly costs, and the amount of time required for the process to be completed.