When trying to deploy a new Integration via Integration Builder or the Administration Console, you get the question "Do you want to Replace existing Integration?" although the name you have given to your new Integration hasn't been previously deployed.
Integration Platform, with already at least 1 Integration deployed.
The customer has manually edited the Integration File (.btin), which has ended up creating 2 Integrations with the same Integration "IntegrationFile ID" and "ID":
You can easily find this out by editing both the affected Integration Files (the new one, and the already deployed one) with an advanced text editor such as Notepad ++.
In the first lines you will see the IDs of these files "IntegrationFile ID" and "ID".
If these ID's are the same, you will need to make them different. After you modify them, you will be able to publish the new Integration
An alternate solution to fix this is to go to File > Save As on the second integration. This creates a new ID on the file. You'll be able to deploy this integration normally.