My phone currently just shows one notification for every notification I add in the app for an event.
You can add additional default notifications in the Google Calendar app.
Inside the app, open the Settings menu. Then tap on the calendar you want to add more notifications to. You'll see a screen like this (this is for my calendar named "Events").
If you tap on "Add another notification" there you can add as many notifications you'd like, up to one minute before the event starts.
This will result in changing the defaults for every new event you add - for existing events, you'll have to edit them individually to add more notifications.