Is "password knocking" a good idea?

With port knocking, you have to "knock" on specific ports in defined order to expose a port on which service is running.

How about password knocking? For example you have three passwords: A, B and C. None of them is correct by itself, but entered one-by-one in this order they will grant you access.

Some scenarios to make this idea clearer:

Scenario 1.

• You: Password A.
  
  
  
  • Server: Invalid password.
  
  
  
  


• You: Password B.
  
  
  
  • Server: Invalid password.
  
  
  
  


• You: Password C.
  
  
  
  • Server: Password accepted.
  
  
  
  

Scenario 2.

• You: Password A.
  
  
  
  • Server: Invalid password.
  
  
  
  


• You: Password C.
  
  
  
  • Server: Invalid password.
  
  
  
  


• You: Password B.
  
  
  
  • Server: Invalid password.
  
  
  
  

Scenario 3.

• You: Password A.
  
  
  
  • Server: Invalid password.
  
  
  
  


• You: Password B.
  
  
  
  • Server: Invalid password.
  
  
  
  


• You: Password B.
  
  
  
  • Server: Invalid password.
  
  
  
  


• You: Password C.
  
  
  
  • Server: Invalid password.
  
  
  
  

Scenario 4.

• You: Password A.
  
  
  
  • Server: Invalid password.
  
  
  
  


• You: Password A.
  
  
  
  • Server: Invalid password.
  
  
  
  


• You: Password B.
  
  
  
  • Server: Invalid password.
  
  
  
  


• You: Password C.
  
  
  
  • Server: Password accepted.
  
  
  
  

I can't think of any drawbacks of this method over regular single password login. Moreover, it makes dictionary attacks exponentially harder with each added password.

I realize it's security by obscurity and doesn't abolish the need for strong passwords. Password sequence itself is as strong as a concatenation of passwords used. Added security in this method comes from unexpectedly complex procedure.

Is it a good idea? Is it a better idea than classic password?