There are three ways to handle this scenario.
Add another answer:
Just because a question has an accepted answer doesn't mean you cannot come along and write an even better answer. The accept only means that the answer solved the asker's problem, but this doesn't mean the community won't come along and upvote your answer well beyond the accepted answer.
Edit the accepted answer:
Another option, if you're sure the asker won't change the accepted answer, and it's important that people be aware of the changes, you could edit the accepted answer and add a new section in it with the new, relevant material. You could say that the above information is outdated and include the new information below.
You could also just add a link to the new question. See below:
Write a new question:
As you mentioned, this is tough, because you don't want it to be marked as a duplicate, but if the new question highlights the fact that things have changed, then the question is less likely to be closed as a duplicate. For instance, a question about privately browsing in Firefox 1.5 will have drastically different responses than a question about privately browsing in Firefox 15. As long as it's clear that the two questions are different, this shouldn't be a problem.
Also, the old question will still apply to anyone using older technologies.