Only one iCloud acount can be your primary account. I have mine set up this way, my secondary account has Mail, Reminders, Contacts, Calendars and Notes. Those apps will display with both iCloud accounts and can be used separately but both will show in the app.
Your primary iCloud account will show Safari ( syncing bookmarks ), photos, documents and data, back to my mac and find my mac as well as those others mentioned above. As for apps and music, they will sync to other devices as long as you use the same iCloud account for their purchase.
I use my accounts separately on my devices ( phone and iPad ) one syncs with the primary account on the mac which is the one my wife and I share, the secondary one syncs with my phone only and that account on the phone backs up separately to iCloud since it is the primary on my phone.
The other way to do this is to create a second user account on your mac and make the other iCloud account as the main one. I had done this for a while but later OS 10 versions allowed for different iCloud accounts to be displayed in Reminders, Contacts, Calendars and notes so I no longer had to log into that user to access those. So I deleted the separate user. Now if more than one of you are using that computer then you might want to have separate user accounts set up.