We're using the LogUnsubEvent API call on our custom preference center and noticing the opt outs are happening at the Enterprise level. Is it possible to perform these opt outs at the BU level?
How it's written will depend on the language you are using, but yes this is possible. You will just have to ensure to list the 'Client ID' as the final part of your call which will represent the MID of that specific business unit. Below is an example using AMPscript:
SET @client = CreateObject("ClientID")
SetObjectProperty(@client, "ID", [Insert MID of specific BU here])
SetObjectProperty(@client, "IDSpecified", "true")
SetObjectProperty(@sub, "Client", @client)