I want to install two instances of Ghost on one server. One install will run in the root (http://domain.com) and the other should run on a subdirectory (http://domain.com/second). The server is running on Apache.
Should this be possible or will Ghost get confused about certain requests and should I just install both in their own respective subdirectory?
As long as you tell each version of Ghost what it's respective URL is, it'll be fine - there should be no conflicting routes by default, although you could end up creating conflicts if you for example created content for the route /second/ on the root install.
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