Water boils at 212°F at sea level whether the boil is spitting volcanoes or the surface of the wort is just moving. Applying too much extra heat to the bottom of the kettle doesn't change the boil temperature but will increase the intensity of the Maillard reaction on the extract at the bottom of the kettle.
You can reduce the amount of heat to maintain a boil and use the late extraction technique. Add enough DME and/or LME to have a specific gravity of about 1.040 for the volume you are boiling. A specific gravity of 1.040 supposedly optimizes hop oil isomerization. Add DME first then LME. LME has already been cooked and will darken the beer more than the DME added at the beginning of the boil.
Add the remainder of the extract at or near the end of the boil. The late extract does not need to be boiled, just dissolved. At 171°F sanitizing occurs in less than a minute. The timing of flavor and aroma hop additions may determine the best time to add the late extract.