Hi Tim,
Apologies for responding with questions on your question :). Would like to clarify few things.
By multiple tenants do you mean, they have multiple Azure subscriptions (CSP/PAYG) associated with different tenants ? (very common for CSP customers, where CSP sub is associated with CSPs own tenant (aka directory) and Cx's PAYG with their own tenants).
When you say "Azure Active Directory is currently replicated from on-premise to the CSP tenant", I am assuming you mean the on-prem (traditional) Active Directory is synced to this tenant perhaps?
Regarding the consolidation question, "Azure AD Domain Service (AADDS)" is a managed version of traditional AD. Do they have this AADDS instance in CSP tenant and the ask is to move to PAYG tenant ?
Just for the sake of clarity:
AD = Traditional AD (which provides LDAP/Kerberos/GPO etc etc)
AAD = Tenant which is used for IAM for Azure/Office365 etc - Azure Subscriptions are associated with a tenant. (can only be linked to one AAD at a time)
AADDS = a Managed version of traditional AD running in Azure where we (Microsoft) manages domain controllers and offers the traditional AD Service.
What aspects of the identity services above needs to be consolidated ?