There is a question that I have an answer to but it has been closed by several respondents as a duplicate and pointing to an answer. In my view the source duplicate is very specific whereas there are more general answers available. It seems that I can vote to reopen the question but with no opportunity to explain the re-open vote. So if I cannot give reasons against the closure why would anyone remove their vote to close?
Here are your options, in somewhat of a preferred sequence:
Make a regular comment on the question, stating why you want to re-open the question. This could include a brief description of your solution, or just stating why the question isn't a duplicate. Don't just state that you want to answer it, because the reason for duplicate closure in the first place was to avoid duplication of content.
This will push the question into the Reopen Review Queue for other 3k+ users can vote on it. They'll see your comment and make a decision based on that.
You could garner support more quickly by joining the chat room and talking to regulars there about your proposal.
Failing (1) above, you can join the chat room and ping one of the moderators who commonly hang around there. Then explain your situation and I'm sure it will be opened without hassle. Their voting power for reopening is binding and doesn't require other contributions in support.
Post a question on Meta.TeX.SE specifically pointing to the question, stating your reason for re-opening. Since your question deals about the main site, this is perfectly acceptable and, again, is an attempt at garnering support for your cause.
Of course, your motivation stems from support of the community and that should always be welcomed, so you're bound to have success with any of the above options, as long as the reason is legit.