mashed potatoes - fixing undercooked potatoes
I would suggest microwaving them on to complete the cooking without getting them waterlogged, unless you have a huge volume of potatoes.   They should still be quite hot from the previous cooking, so should not take long to begin cooking in the microwave.

If you don't have a microwave, you could try continuing to boil them, but you don't want to add cold water and have the starches begin to crystallize, so I would try to keep them as warm as reasonably possible while bringing the water to a boil in an electric kettle or another pot.