A salt is not for adding extra secrecy. It's for making it take more work to solve a large number of passwords at once. It doesn't need to be stored separately

A salt is not for adding extra secrecy. It's for making it take more work to solve a large number of passwords at once. It doesn't need to be stored separately to do this. What you're thinking of is a secret-splitting scheme; where you split a secret among multiple parties, where you need the information from both parties to reconstruct the secret. That's a valid cryptographic technique, but that's not what's meant when you say "salted password". The problem is, for passwords, that approach isn't really workable. Whatever machine is verifying the passwords will need access to the full hash to do so, so if it's compromised, you could get access to the full hash. I suppose you could split the verification into two parts, on two separate machines. Each one would have it's own password database, with independent salts, and the machine trying to authenticate the user would request verification from each of the other machines before allowing you in. However, that would make your password system slower and more fragile; now if either of those machines goes offline, your login functionality breaks (and yes, you could do a "two out of three" system to avoid that, but now you're talking about tripling your hardware requirements just for your password verification system). Really the best bang for your buck will come from (a) securing your system so that it doesn't reveal your password database in the first place and (b) using bcrypt, scrypt, or PBKDF2 to make brute forcing a database that is disclosed much more difficult. It's far more likely that you will build a secure system by following basic security practices like isolating services and giving each the minimum privilege that it needs, doing code review, keeping inessential services off of important machines, using prepared statements rather than building SQL queries from user-supplied strings, and so on, as well as using off-the-shelf security components that have been well tested like the above hash algorithms, than you will by designing your own password system using some novel technique to spread the secret out among multiple machines.