How to create a new copy of a theme currently being used?

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I assume you do have full access to admin?

Several options I came up with without much thinking:

  1. Make an archive with modified copy of theme, install it through file upload. Obviously this is easier if you have copy of theme, otherwise you might have to build it file by file from sources accessible in theme Editor.
  2. Create child theme for original theme, install via file upload. Might or might not fit, depending on what you want to do.
  3. Create a plugin that will on activation copy theme to another folder and modify its detail. Little bit too geeky.