For now you could simulate this with either quasi-streams:
http://www.multichain.com/developers/creating-data-streams/
Or by using an asset (with zero asset units created) to represent each customer, and performing a follow-on issuance for each update of that user's details. (Use listassets with verbose=true to see the full history of a particular asset.)
We are currently laying the architectural foundations for a new set of "streams" APIs which will work as a more natural abstraction for this use case, but hopefully the above will let you get started.