Is it a Sky+ box, or a Sky+HD box?
The Sky+HD box does have a "single feed mode" as part of the new EPG, but the Sky+ box does not.
Whichever kind of box it is, if you only have one feed, then as you have found you cannot use it to its fullest. e.g. You cannot watch one channel while recording another, or record two channels at once.
If it's a Sky+HD box, you can at least record what you are watching, & you can have it perform unattended recordings while it is in standby.
With only a communal dish installed at the property, and only a single feed provided to your flat, there is not much you can do. Having another feed installed to your flat could be a possibility, but in all likelihood would be extremely expensive.