If you have created your own Dropbox app, you can only connect to it from one domain and for 1 Dropbox account. However you can increase the number of accounts/domains without applying for production by clicking on 'Enable additional users' in the App Console (https://www.dropbox.com/developers/apps).
It is also possible to just use the default app of the plugin, in that case just remove the App Key and Secret from the plugin settings page.