I've done two cars, with two different methods. Biggest issue is the windshield. Even with the roof cut off, most cages won't slip in behind the windshield. Odds are high that a well fit cage won't clear all the floor bits enough to make it under the windshield.
Years ago, we moved a cage from one Honda Civic to another. Had to cut the cage in half at the main hoop to fit it in. We cut the roof on the new(ish) car at the C and B pillars and peeled the roof back like a sardine can. We cut all the forward tubes at the main hoop as close to the main hoop as possible. The person running the saw had to be very careful, slow and precise. And single nick in the main hoop would mean just building a new cage. Ground down the remaining tube stumps and weld from the hoop - again, very, very carefully. Left just a bit of the old weld in place - mostly to prove we didn't grind into the main hoop tubes at all. Then we notched all the forward tubes to the main hoop - ended up losing less than an inch total. Put the two parts of the cage in the car, through the opened roof, tacked it all together and welded it all up and welded the roof back down. Overall, a very painful process and I would never do it again.
I also helped Kyle move a Kia roll cage from one car to another identical car. In that case, he complete cut the roof AND windshield off. That one was easier - the cage was untouched. Just had to weld the spreader plates into the new car. Granted, it was a pain to the get the windshield angles 100% correct when those were welded back. In that case Kyle needed to replace the windshield anyhow, so it made the decision to cut really easy.
The second method was far better.
Apparently my name is really "Craigers". Who knew?
We might be yellow, but at least we are slow
I'm a WINNER!