I want to purchase a WordPress theme...it is used by a competitor. Can they make a formal complaint that I have copied their site...I would want to modify it to look a little different, but it would appear very similar initially...
Here's what I recommend. Since you plan to nearly duplicate the theme of a competitor, you should turn your computer into your own private web server and run anything on that.
The advantage here is the server is only accessible by your computer and no internet connection is required by you to access it. Easiest way to get one is to download apache and set it up.
If that does not work, then rent an online server and contact the administrator to set it up so that computers from your network are the only ones allowed in (while other users will get some sort of access denied message). This will be a bit easier if you go for a virtual private server or dedicated server but those options may be more expensive.
While my idea might seem somewhat sneaky, you're actually doing two sets of people a favor. you're doing guests a favor by not making them see undesired webpages when they try to access your site at the same time you're making one of many updates. You're also doing your competitor a favor by not making consistant minor tweaks to the site where most of those changes could result in duplicate pages of that of the competitor.
When you are editing, you want to modify it to look different to the point where there's no chance you're copying your competitor. I mean if you want to use a similar set of colors, that's no problem. Heck, nearly every quality website I see has a basic color theme of using black text on a white background.
I think the most amount of copying you can do without getting in trouble is about 10 to 25%, but what I strongly recommend is to use completely different text and completely different user interface layout. For example, if your competitor has a series of buttons on the left and talks about boats, you can make a site with a series of buttons with bigger spacing on the right that talks about cats.