A330-300s also do not have fuel dumping. MTOW 233T MLW187T. You can land up to MTOW after performing the overweight landing checklist.
If engine out and heavy, or even with both engines running it may be required to start APU to supply packs or switch off packs for Go-around performance, combined with a flap 3 approach.
I assume it will be something similar with the 320.