Symptoms

There are two K2 servers and one SharePoint server. The K2 app from the one K2 server is deployed to a site collection on the SharePoint server, but they want to be able to use both K2 apps on the same site collection (to be able to connect to two K2 servers on one site collection).
 

Diagnoses

You cannot add two K2 apps to one site collection. However, with certain conditions (like a version higher than 1.0.1 of the K2 app for example) you can add two K2 apps on the same SharePoint server by putting them in two different Web Apps.
 

Resolution

We eventually resolved this by re-running the AppDeployment.exe on the SP2013 server as the K2 Service account for the K2 DEV (other K2 server) system. It needed administrative permissions.

Once we deployed the K2 DEV app, the K2 Production app was overwritten but that was acceptable.

You can technically speaking run two different K2 apps on the same SharePoint server, but they should be deployed to two different Web Applications (each with their own App Catalogue). This is definitely supported in 4.6.9, however it is also possible with the K2 for SharePoint 1.0.1 app.

You cannot have two K2 apps deployed to the same App Catalogue / Site Collection.