No, you can not. With your Greek travel documents you are allowed to travel inside the European Union for a maximum time frame of three months in six months. You are not allowed to stay and work in another European country, because you have already asylum in Greece and are supposed to live there. According to European law it is only possible to have asylum in ONE European state. If you already have an asylum status in Greece but for example apply for asylum in Germany, it is very likely that the German authorities will reject your asylum claim and decide that you should be brought back to Greece. You can appeal against the deportation decision. You will need to find a lawyer for that and you only have a short period of time to do it (normally one week). Please note, that at the moment German courts are completely overwhelmed with appeals, so it might take more then one year before there is a decision in your case. Nobody can really predict how a court case like this might end. But remember that people are sent back, in spite of the challenging living conditions in Greece. Even if you might win the court case, you will not get asylum in Germany. The German authorities will only suspend your deportation to Greece and grant you a short term residence permit, called "Duldung". This residence permit has to be renewed every 6 or 12 months and if the conditions in Greece have improved in the meantime, the renewal can be refused and you can then be deported back to Greece.