I have several Apple IDs associated with my computer. However, you can only be logged in as one at a time. One way to do this is to have separate User accounts on the computer, if it is for that purpose, as @zenvelo describes… which is what I did when my son and I shared a computer for many years. Each of us had our .mac IDs on our user accounts for .mac mail, iDisk and iTunes, etc.
Now I am engaged to a man who has 2 Apple IDs because Apple doesn’t let you merge those when they make changes to the system, so he had one that was just an iTunes account, and then when he got a Mac with a .mac account, they didn’t let him use the same ID. We also have a shared Apple ID, and I have my original Apple ID from when iTools was free in 2001.
SOooooooo… Only my personal ID is in the System Preferences for iCloud. But to share iTunes Libraries, etc., all those accounts are authorized on my computer in iTunes. And for App purchases in the App Store and iTunes Store, I have to log out and log in as the other user to purchase apps that were originally made with other Apple IDs.