Android - How to keep two versions of an app installed?

Yes. It is possible.

Change the package name in your Android manifest or app build.gradle.

Example:

Application version 1

app build gradle:

defaultConfig {
        applicationId "com.example.application.appone"
        ...
              }

manifest file:

<manifest
    package="com.example.application.appone">

Application version 2

app build gradle:

defaultConfig {
        applicationId "com.example.application.apptwo"
        ...
              }

manifest file:

<manifest
    package="com.example.application.apptwo">