Is it possible to establish an app whitelist for installers not found on the App Store/available through VPP?

I work in a shop which necessitates strong administrative controls. However, a few teams use apps which are only found outside of the App Store and require fairly frequent updates - those updates themselves require downloading and fully installing the new version instead of a helper tool.

Without allowing the user to be an admin themselves, is there a way to essentially "whitelist" the apps to allow their accounts to install specific apps and not need our admin user/pw?

Thanks!