Client expects me to be ok plagiarising a site

A client asked me to use another site as a template for theirs. I built a site using that cue, replicating the look and feel but not making it exactly the same.

Client: The font is different than the example! Change the font.

I changed the font to the exact same.

Client: The menu looks a little different.

I copied the menu exactly, clenching for what I knew would come next. Little by little, the client kept asking for incremental changes to make the site EXACTLY like this other one, asking me to basically steal the design by degrees.

 I’m thinking of shifting to daily billing for revisions.