If your loan amount is high enough (usually $175k+) You could refinance with your existing lender (or a new lender) and instead of paying closing costs and getting the prevailing low interest rate for what you qualify for, you'd take an interest rate usually .25-.375% higher and the mortgage lender will pay for most if not all of your closing costs.
When you are refinancing and have a 2nd mortgage which you are not paying off, you need to subordinate the 2nd mortgage, meaning ask permission for it to remain in 2nd position after the new mortgage is made. Essentially the 2nd mortgage is underwritten again, requiring an appraisal, underwriting approval for the new 1st mortgage refinance, etc. Costs an additional $200-300 and depending on the 2nd mortgage lender adds anywhere from 2-6 weeks to the refinance process (if your 2nd is Citi, it takes about 3 weeks), as these days subordination departments have a high volume of work for the amount of staff.
Unless you are able to refinance, you could try to negotiate with your current lender but they'd likely refer you to their refinance department. If you don't have much equity, which could make refinancing difficult, then negotiation/modifying your existing loan may be your only option.
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