How can I gain permanent residency in Greece to move in with my partner if we are an unmarried couple?

In order to accurately answer your questions, more information is required regarding the residence status of your partner and the provided residence and work permit he is entitled. Furthermore, please be advised that the permanent residence permit granted to property investors gives you the right to stay in the country but does not provide access to the employment market (work permit). You should further consider the possibility of concluding a cohabitation agreement since Greek Law recognizes the cohabitants as family members or the option of a digital nomad visa as per your individual residence permit if you fulfill the requirements.