Of course it is "possible." Just like Dr. Frankenstein worked at home. Whose project, echoing the question by gigleus, had some major reliability and safety concerns, to say the least.

Maybe, more like the kind of "home brewed" projects such as, say, turning a 20 year-old pickup into an all electric vehicle or into a dragster with a twin supercharger "454" motor and huge racing slicks, or turning it into a four-wheel-drive, high lift monster truck.

Can be done, but would you want that for your daily ride?

Hvtech has an interesting suggestion for owners of old Jenn Air "modular" cooktops and stoves. However, while Jenn Air made numbers of smoothtop radiant electric cartridges/ modules, I cannot recall ever seeing an induction cartridge.

The burner control systems were just too different, which is a big reason why nobody makes (or will make) plug-and-play induction modules that can fit into the top of a coil-burner stove or into the supports beneath an old smoothtop. The older style electric stoves used electro-mechanical potentiometer/rheostat burner controls. Making those work with the digital microprocessor controls used by induction burners is pretty complicated. (AFAIK, only Miele and Garland/Mantowiac induction burners have potentiometer controls; their products cost $$$$)

This is what Homepro meant with the comment about different control technology.

For a Frankenstove, you would need to rip out the old control systems and wiring, assemble a set of the microprocessor-driven control-boards required to operate the induction burners, and then figure out how to reprogram them and convert them to work with a rotary knob interface.

You also would need to build a fan system to keep the induction electronics cool, which is something nobody did with electric stoves 25 years ago. You'd also need to build in enough space for clearance from the oven part, too.

All of that would be for naught if your old stove has the oven vent in one of the rear burners as numbers of electric coil stoves did, back then.

The closest thing to "plug-and-play" induction burners are the commercial "drop-in" induction burners from the likes of Cooktek. In theory, you could carve up or build a new stove-top to hold four of them, rewire the range, and cut holes in the backsplash to mount their control modules. That would cost you around $4k to $5k in parts, which is a whole lot more than just buying a new induction range outright. For that kind of money you might as well be looking at the ultra-premium priced induction ranges from the likes of Dacor, Viking and Miele.

And a Cooktek style solution would still require you figure out how to get enough clearance below the burners for their cooling to operate while you are using your old stove's oven.

So, no plug and play solution here.

As homepro noted, some folks have pulled out old non-functioning coil burners and placed a couple of portable induction cookers (PIC) over the holes, That will raise the level of your cooking surface by two or three inches which may or may not be a problem. The size of the PIC casings is large enough that it will be next to impossible to fit more that two PICs on top of the old stove. Depending on how many burners you use at a time, that may or may not be a problem, as well.

There are some limitations to working with the less expensive PICs (which would be most of them).

In an older kitchen, there might be some problems finding enough separate 120v electrical circuits (PICs can draw so much current that you will blow a circuit breaker by running two on the same circuit at the same time -- same thing with a microwave, btw). One nice thing, though, is that many electric stoves from 25-years ago had an extra-120v outlet on the backsplash and, running through the stove's connections, that outlet will be on a circuit separate from other kitchen outlets.

If that kind of solution interests you, you could check out the discussions in the cookware section at chowhound.com where numbers of folks like paulj and have reported putting PICs on old stoves and several others have decided to dispense with stoves altogether. Also, look over the blogs on induction at www.centurylife.org. For a discussion here on using PICS, you might check out this thread if you have not already seen it: http://ths.gardenweb.com/discussions/2324992/portable-induction-cooktop-and-cookware