U.S. to join P-4...but will it be P-4 as we know it?

As many will have seen, Susan Schwab announced this week the U.S.'s intention to join the Comprehensive Trans-Pacific Strategic Economic Partnership agreement, aka (at least here in New Zealand) the P-4 Agreement or P-4.  P-4 is a pretty interesting agreement.  The current parties are New Zealand, Singapore, Brunei, and Chile.  Of note is that P-4 is a very comprehensive agreement in comparison to many, and that it has an open accession provision, meaning that other countries willing to agree to the terms of P-4 can join the agreement.  Until now no country has sought to join the agreement, presumably in part because of its comprehensive nature.  All that may change now, however.  Assuming that the new administration decides to proceed with these negotiations next year as Schwab intends, it seems highly likely to me that the U.S. will insist on its FTA template, which will entail a ratcheting back of the scope of P-4.  How will the current members respond?  The U.S. already has FTAs in place with P-4 members Chile and Singapore, and New Zealand has been very anxious to form an FTA with the U.S. for several years now.  One doubts Brunei will sway the balance.  If the P-4 becomes the P-5 based on more of a U.S. FTA model, other U.S. FTA partners will presumably be keen to join in.  This may be the avenue by which the U.S. shapes the core agreement underlying an ultimate APEC free trade area.  In any case, it will be interesting - if it goes forward - to see if the scope of the agreement is renegotiated such that the commitments are less comprehensive than at present.  Has that ever happened before, to anyone's knowledge?