Is there anybody else who has access to the ftp-folder of your website?
If you are sure, that nothing has changed from the website already live on the www, and you are sure, your client didn`t change anything via inbrowserediting or manually added some code to the root directory (this should be, where your index.html is located), you can upload your actual muse to this as you did before.
For safety reasons, before replacing the existing website, you should create a new folder on your ftp and drag everything into this folder from the existing website!
If you provide a link – we have some coders here in this forum who could detect your source code and may tell you what might have happened.
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Really, you should believe the moderator. This is no official support channel from ADOBE.
This is what one member of the forum suggests.
What´s the answer to my question from above? Who else, except you, has access to the ftp-Server.
You should contact this person/company/organisation.
If you are sure, that nobody except you has access, do as suggested above.
Save the old site to a subfolder that you have to create manually with cyberduck/filezilla or similar ftp-programme.
Then, and only then you could delete this "old" site before you upload the new .muse to the original root directory.