Hey there, jjkatz.
Welcome to the Apple Support Communities! Thanks for your question about being able to disable the notifications associated with pending updates. We'd be glad to see what we can do to help you out.
Are these notifications just letting you know that the apps have been updated, or are you getting them to tell you that updates are available? Do you still get the notifications if you go to System Preferences > Software Updates > Advanced and check all of the available boxes? More info on what all is detailed in those boxes is available in Keep your Mac up to date.
Let us know what you find out.
Be well.