Actually, the answer is that most often data can be added. A multi-session disc is usually the default for most burning programs. Multi-session discs that have been finalized cannot add data. If you use a burning program with disc analysis features, such as Nero, the program can tell you whether the disc can have data added.

If I understand you correctly you had started a burn session and then interupted it and want to know if you can still add information to it?  More than likely not.  When you burn disks the software puts check points if you will so that it knows where to start again.  If you interupted this they wont be there and the disk will either show as not blank, or y our software will try to write on the used space again.

If you want to know if you can multi-session a DVD then yes you can, but some players may have difficulty reading those disks.  I have never had an issue doing this yet.  Just make sure you enable it in your software to multi-sessions.

You cant multi-session a disk that has already been finalised.