You can concatenate your fact tables into one table and there will be no synthetic keys, just 4 common fields.
Or you can create your own unique key to link the tables:
key1 as table1_key1,
key2 as table1_key2,
key3 as table1_key3,
key4 as table2_key4,
key1 & '/' & key2 & '/' & key3 & '/' & key4 as key;
To avoid the synthetic keys you can rename the fields by which you dont want to link the fact table.
renaming the field avoids the synthetic kyes.
You can concate the tables as Masha told.
You can create the link table to connect the fact tables with the more than one field.