Is it possible to extend the range of an electromagnet? How would one do this?
Extend the range? Why do you mean? If by range you mean the distance at which it exerts a force, well, that's already infinity.
Crank up the juice.
Ummm...yeah. I'm pretty sure he means he distance at which it produces a measurable, non-negligible force that is capable of doing something. If so, then russ waters is right. The larger the current in the coil, the stronger the magnetic field will be at any given distance.
An electromagnet with iron as a core will saturate at some value of the field strength. At that point you get no more help from the iron in increasing the field strength and cranking up the juice will have much less effect. At this point it's better to increase the diameter of the core and the coil. (and crank up the juice as well to keep the field strength constant).
a 1 cm^2 coil with a field strength of 1T will produce the same force at 5 cm as a 100 cm^2 coil with the same field strength will at 50 cm.