First off I’d like to make sure to clarify some terms.
We use application when we are talking about applying for a developer account
We use Twitter apps to discuss the apps that you create and manage that you pull your tokens from.
I’d be curious to hear how you are defining installations to help clarify this conversation.
It is a best practice for you to use a different Twitter app and set of tokens for each of the different use cases that you may have, keeping in mind that multiple clients might be using your app for the same use case. You can list this use case within the app management dashboard on developer.twitter.com.
Ex/ you have a Twitter app that is being used to allow customers to search the Twitter database for Tweets related to a query. You can make requests via this app for multiple users as long as it is for the same use case.
You should be able to perform all of your tasks related to your organization or personal development with a single developer portal account. Please do not apply for multiple different organizations.
If you need to make requests on behalf of other users, please implement the 3-legged oauth flow to have your users authorize your Twitter apps. If you have users go through this flow, it will provide you access tokens to make requests on their behalf.