Security of adding letter in front of passphrase

I am wondering about the security of adding a letter in front of a long passphrase to help me have different passphrases for each site I use while not requiring me to remember several different N word sentences.

E.g., if my phrase is the classic “correcthorsebatterystaple”, would it be ill-advised to add, say, “f” for facebook, “g” for gmail etc.? I could imagine it both adding one extra character of complexity to the phrase (good), but if inspected by a human, that pattern may be obvious (bad).