Is it possible to update a published site from an amended copy of the original design file?
Means, you have a .muse file? What has to be updated? The muse file?
Normally, with a "connected", yet original file, muse checks if there are some changes in the published site.
You get asked, wether to merge those two versions, view it first and then merge or not to merge.
If you open a copy of the .muse which has never been connected to the web, you normally get this warning right in the process of publishing.
If none of these cases is your case, update your .muse and publish it. If you get asked to upload all data or only changes chose whatever you desire.