Nowadays, addresses can be generated that require a combination of multiple private keys. Since these take benefit of newer features, they begin with the more modern prefix of 3 instead of the older 1, as mentioned earlier.
These can be imagined of as the equivalent of writing a check to two parties - "pay to the order of two persons in one go" - where both sides must endorse the check to obtain the funds.
The actual condition (the number of private keys needed, their corresponding public keys, etc.) that must be met to spend the funds is determined in advance by the person creating this type of address, and once an address is created, the requirement cannot be changed without creating a new address.