Parametrize linked service

Our issue spans over multiple factories as we need a way to parametrize the authentication method for both using user managed (UMI) and systems managed identities (SMI) as well as using different credentials for the respective UMIs. The linked service we use is of type AzureDataExplorer.

Ideally we would like to have the following architecture:

• factory_1 (connected to repo) using linkedService X with SMI_1
• factory_2 (NOT connected to repo) using linkedService X with SMI_2
• factory_3 (connected to repo) using linkedService X with UMI_1
• factory_4 (connected to repo) using linkedService X with UMI_2
• factory_5 (NOT connected to repo) using linkedService X with UMI_3

All of the above factories should be based on the same repository either with a direct connection to it or we deploy to them using templates but still using the same repository. Currently we have setup factories_1 and _2 using SMIs and they are working fine but we are having trouble setting up the remaining factories because we cannot manage to parametrize the authentication method of service X.

The question is whether such a setup is even possible in ADF and if so, how would we achieve this parametrization, i.e. what would the linked Service JSON look like? We would ideally like to achieve this set up using global parameters as we do not need to specify a different authentication method per pipeline but just per factory.