The more I use my Android Kit Kat 4.4.4 Note 3 operating system, the more clunky it seems.
On my Note 3, in order to add multiple alarms on the same day, you must first scroll down to the bottom of the alarm page, and re-name the alarm (default name is "alarm"). Once you provide a new name (such as "Alarm2"), and after you set the time and day, when you hit SAVE, a new alarm can be created on the same day as another alarm.
Non-intuitive!