The Port Authority has nothing to do with Penn Station train operations, NJT, LIRR, or MN, only to an unrelated and land-locked PATH.
Thru run to where ? There is no place to send them except Sunnyside or back to Jersey and Sunnyside is pretty well full mid-day. Nothing is being done east of 7th Avenue Manhattan, beyond the scope of the Gateway Project. If you want to build a fifth track across Manhattan, the East River, and out to Jamaica, find $30 or 40 Billion. You can't thru run MN trains to the NEC and turn back anywhere until South Amboy, and definitely not Newark, which serves no purpose. The peak services of MTA and NJT run in opposite directions toward Manhattan.
Metro North will use LIRR owned station slots vacated by the LIRR when Grand Central Madison opened a year ago, and either proceed to West Side Yard or back to New Rochelle, or wherever they came from. Their station dwell time is seldom more than 10 minutes. It is not like MTA trains sit around for a half hour and LIRR is a lightly used railroad ready to accommodate more traffic.
https://www.irum.org/20140807_Amtrak_NYP_Thru_Running_Assessment.pdf
"Further, current operations are optimized around the existing terminal infrastructure with its two main support yards serving in a critical role to achieving very high levels of performance. Without investment in new station facilities to compensate for the utility provided by yards, the introduction of a through running revenue service with commuter trains would lead to fewer peak period trains and/or less reliable operations under representative service scenarios evaluated. Potential"