I'm regressing just a bit and may be missing the point of the original question because don't know what a third party payee is.
However, if the example involves Mary Beth depositing a check payable to John which John endorsed prior to Mary Beth's endorsement and presentment, then I would say the bank is entitled to an exception hold based on reasonable cause to doubt collectibility. My entire argument hangs on model form C-13's listing of:
--We are unable to verify the endorsement of a joint payee.
as an acceptable reason for an exception hold. The validity of the prior endorsement which it did not witness is no less important to the depositary institution as the validity of a joint payee's endorsement which it did not witness.
Before anyone cheers, please consider that the maximum hold you could gain from this maneuver is to the eleventh business day following the banking day of deposit. On the other hand, the drawee bank has up to three years to return the item for a forged endorsement. This isn't a workable risk management tool.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.