How do I (re)design my corporate website in WordPress without downtime?

Yes, it is possible – even more – this is common practice. But…

  1. When creating new site, you should never do it directly on production server – during development the site is not as secure as it should be.

  2. During development the site should never be public – you’ll have a lot more work if search engines will index such temporary site.

  3. You should take care of all URLs from old site (people very often forget about this step).

So I would recommend to:

  1. Create new site offline, migrate all contents, take care of all URLs from old site.

  2. When the site is ready, upload it to the production server (place it in subfolder, because uploading may take few minutes). Move old site to subfolder and move new site from subfolder to root folder (these 2 operations should be very quick).

  3. Secure the new site.

  4. If everything works OK, dump old site and remove it from server (never leave old site on server – it would be a huge security flaw).

  5. Monitor any 404 errors and fix them.