Quote from: 12inchdick on July 13, 2014, 12:40:00 PM

If you give one of the private keys of a multisig address to another person, can he/she regenerate your other private keys because your wallet is deterministic?

No.
The private keys are calculated based off a seed by taking a hash of the seed. Since a hash is a one-way function, the resulting private key doesn't give any info about the seed, and thus doesn't provide any way to obtain other private keys that would be generated by it.
Here's a basic example (not actually the way most deterministic wallets work, but a simplified example): To generate a private key take SHA256(string + n), where n is an ASCII-coded number that starts from 1 and increments as additional keys are needed.