I am looking for possible ways of attacking a modified Vigenère cipher. Let's say we have two keys e.g. 'stackoverflow' and 'Vigenère'. The V cipher starts with one of those keys but switches as soon as it would create a doublet [so the next plaintext letter would decrypt to the same ciphertext letter like (example for ciphertext:) 'LDJAAIWE' or 'FMGGBPV')].
How is it possible to attack this if you don't know the content of the text?
Since you don't know when the change of keys happens, you can't use the normal hill-climbing attacks.
Obviously, you can get some information from the rarely occurring doublets. They would let you know that the previously used key and the newly used key encrypted the plaintext letter to the same cipher letter. But those doublets would be very rare, and you would not know which key was previously used and at which position inside the key you were.
I am not sure how you'd try to attack this unless you try some dictionary attack and drag the words along the text to see if you can spot anything.