A Payable Through Account, and I might be oversimplifying (and if so, someone will correct me, I'm sure,) allows a customer to transact somewhat directly with a correspondent bank through the account 'their' bank holds with the correspondent.
From an AML and KYC perspective they're frowned upon. You can see why; Bob's Bait & Tackle & MSB is doing transactions through JPMorgan to Citi, but through a JPMorgan account, not their own account.
The very minimum due diliginence that I'd suggest is that only account-holding customers of the bank, those on whom you've done adequate KYC investigation, be the only once I'd even consider eligible for that particular convenience. Even then, the policy should be to steer them away from using a payable through account and into something more, trackable....
Just my US$.02