Customarily, when my clients return to me to merely alter something I've already created, they do get a reduced price. Exactly because I already built what they need and they merely want to alter it. This keeps clients happy, which is always the goal.
If they wanted to make a few edits to the existing site, would you charge them a fee based on an entire new site? Of course not. You'd charge them for the edits.
Essentially, for a cloned site, that's all they are asking for - edits and not creation. So charge them a fee based upon editing and not constructing.
I do have "base prices" for smaller, particular, projects and this is explained to clients -- i.e. an HTML email design has a base price. So, if they need an email, pricing starts at [$xxx.xx], then may increase from there based upon the complexity desired. But they will never be charged less than [$xxx.xx] for an HTML email. I stress minimum fee, not "standard fee".
It's essentially a "minimal cost" for the item they are requesting. I know that for every project of this nature I will need to do X, Y, and Z every time. So, I build the time needed to complete those tasks into a "base fee" or "minimum price".
It would not be out of line of you to have a base price for a Wordpress site. That base price should be factored considering the smallest amount of time it would take to throw up a Wordpress site.
"Throw up"-- not design or configure/personalize or any of that.... merely the amount of time it would to take you to create a "canned" Wordpress site and have it live and active. (or I'll use 2 hours at my hourly rate as a minimum, if the time to complete these standard tasks is negligible.)
Then you add your editing fees on top of that "base price" or "minimum fee". The result is typically far, far less than a brand new site keeping the client happy. While at the same time providing you a bit more income than just your editing fees. Having this base pricing allows you to gain some revenue from the client's additional ROI for the new item. While at the same time, NOT charging the client standard fees as if it were an entirely new project.
You can also use your base price as negotiating factors at times... Telling a new client that [project X] has a minimum fee of [$xxx.xx] and pricing will increase from that point, can help to dissuade looky-loos or window-shopping clients. If your base price is too much for them, then their project isn't worth your time.
This is merely how I handle similar matters. I'm not stating it's the "correct" way to do so, only that it's worked well for me. I'd much rather have a client return to me over and over with more work than make a few extra dollars on one project and never see the client again.