The new regulation has no special impact on your responsibilities regarding TPPP customers; eventually, you will have to identify their beneficial owners just like any other legal entity that opens an account with you. If you have a constantly updated list of your customer's customers, you are probably well ahead of the pack. If you require beneficial ownership information on any or all of them it will be driven by an internal decision.
In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.