Separate takes is the most obvious solution, but to add to bit's suggestions:
the first thing is the singer. You can control a lot of dynamics at the source, simply by moving your head back and closer to the mic. Yea, this can change the tone a little but is better than scorching the take.
If the room will allow, and you have a mic/preamp combo that can handle it, back the singer off. I usually start out at about 18 inches normally, but one can do farther away. Remember, distance is the original compressor. Because sound energy is geometric, doubling the distance between mic and source drops the energy by 1/4.
This is one of those things that should be noted when people wonder why so much is spent on equipment - hundreds (or thousands) on a preamp. Where you can get a good compromise on a problem take using a lower-cost, integrated interface it will probably take more time and work. A really nice preamp will have the gain to back the singer off without losing clarity or definition, it will grab the lower volume sounds yet not distort on the louder ones but go into a nice transformer saturation whereas the IC interface distorts or the converters give you digital hash. Forget all the talk of "tone" etc., it is just that good tools will save you as an engineer. I was recording one of the better local fiddle players. She has a really nice violin and while talking shop she admitted it had saved her ... neck many times. A good talent and tool work together. Good tools make your job easier and less frustrating and let you survive your mistakes with reputation intact.
Long story short, try backing off the mic as far as the room and equipment will allow.