Can multiple fact tables have the same structure?
Yes and depending on what you are doing that might be a very good idea. I will use a request table as an example.

Request comes in and goes to a submitted request table. After it gets processed it moves to a pending table. If it gets approved it moves to an approved/completed table. If it gets canceled it gets moved to a canceled table. Having the same table structure allows for the system to easily move data around and for users to easily select data from any of the tables.

While this can also be done with a status column the design of the database and amount of data could make it more desirable to have a separate table for each state.