Yes, migration is supported between the Stratix® III device and Stratix IV E device families. In general, migration between different device families is not supported. The Stratix III device and Stratix IV E device family migration is the first cross family migration option supported by Altera® .
The Quartus® II software does not support migration between the Stratix III device and Stratix IV E device families. You will need seperate Quartus II software projects to generate unique configuration files for each of these device families.