Hi @Garvey :)
I think your question already contains parts of the answer. As you said there is Dublin III. This law says that you can only have one asylum application in a EU country. If you go to any other they will probably send you back. Germany, for example, will most likely send you back to Belgium. I can't tell you though if Belgium will then deport you back to Greece. Some European countries suspended deportation because of the chaotic situation over there.
But if the circumstances in your home country changed for the worse, or if you have new evidence to prove that you need refugee protection, then you can apply again in Greece.
All the best,