I'd be really careful with that (personally I think it's terrible advice, although functionally it doesn't come up *that* often). For example, consider if A began:
Originally constructed in 1835, Charlie lives in a house...That's a modifier error, obviously (the house is the only thing that could logically have been constructed in 1835), but if you look at its meaning the way it's written it technically says that Charlie was originally constructed in 1835. So do you go to B-E trying to preserve that illogical meaning?
A great many Sentence Correction errors are errors precisely because they create vague/unclear or illogical meanings. So if A has an error, A may very well have a flawed meaning, so you'd be looking for choices that protect the mistake. Or it may have an incomplete/unclear meaning, so if you're looking for your understanding of the intended meaning, you might have the wrong meaning and miss the right answer this way.
I've always used this official problem -
https://gmatclub.com/forum/using-a-doppler-ultrasound-device-fetal-heartbeats-can-be-54006.html - to make this point in classes. The right answer introduces a doctor, who doesn't appear in the passive-voice-heavy original. But the whole problem with the original is that you don't have a valid entity that could use this ultrasound device, so you have to "change" the meaning in order to have a valid, complete thought:
Using a Doppler ultrasound device, fetal heartbeats can be detected by the twelfth week of pregnancy.(A) Using a Doppler ultrasound device, fetal heartbeats can be detected by the twelfth week of pregnancy.
(B) Fetal heartbeats can be detected by the twelfth week of pregnancy, using a Doppler ultrasound device.
(C) Detecting fetal heartbeats by the twelfth week of pregnancy, a physician can use a Doppler ultrasound device.
(D) By the twelfth week of pregnancy, fetal heart-beats can be detected using a Doppler ultrasound device by a physician.
(E) Using a Doppler ultrasound device, a physician can detect fetal heartbeats by the twelfth week of pregnancy.
Now, like I said it doesn't come up a ton so it's probably just 'bad' advice and not 'terrible' advice. But "protect the original meaning" doesn't appear anywhere in the instructions, and there are cases where doing so will lead to wrong answers or frustrating thought processes, so I'd avoid that.