Part of this deal, contained in its final sentence, allows not only for Metro North to operate on Amtrak property, but also for Amtrak to operate trains onto Long Island over LIRR trackage. While the announcement says that Amtrak trains from Long Island could continue via Penn Station to Washington or Boston, logically Boston would involve some doglegging between Penn Station and Queens. But add service to the Empire Corridor (Albany), which is also possible without changing directions.
From Albany, NY Times-Union, 1/22/19:
Amtrak trains could serve Long Island
Some Metro-North commuter trains serving the New Haven line could arrive at Penn Station instead of Grand Central, under an agreement between the Metropolitan Transportation Authority, Amtrak and the Empire State Development Corp. announced Tuesday by Gov. Andrew Cuomo.
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Technically what still needs to be ironed out is the power collection systems... overhead catenary vs third rail, and the differences between overrunning and underrunning third rail on LIRR and MNRR trackage. I think that through Long Island-Albany service seems the most logical since dual mode locomotives are already used, and with LIRR type third rail.