No, you cannot have multiple public addresses from a single private key.

However, over 28 million private keys can produce the same bitcoin address. Seriously.

However, the chance of every producing a collision is so astronomically rare that you would have to be bitten by a shark, hit by a bus, shot by a gunman, struck by lightning and win the lottery all within a single day.

Trying to get a collision? Forget it, it's virtually impossible!