Is it possible to join two layers in PyQGIS, on multiple fields?
ie, JOIN ON layer1field1 = layer2field1 AND layer1field2 = layer2field2
If so, how?
I do not think this is possible as this cannot be achieved via the GUI.
An alternative could be to duplicate layer1 which would allow you to join each layer1 with the relevant field of layer2.
Your question uses the "AND" statement which suggest both field joins must be true for a feature to join. With that another alternative approach would be: