The DAAD has a added a flexible program to their scholarship offers. PhD students can choose to spend between one and twelve months abroad, split their time several into shorter stays and/or choose different countries. You can find this program as well as others in the DAAD database. 

Because of the Corona pandemic, deadlines have been extended (End of August 2020 for scholarships starting January 2021). Starting 2021, three application periods are planned.