Tom, it's possible that the four boxed underpasses were used for the four tracks tied to Manhattan Transfer - Jersey City service. Just a guess, but there were two passenger tracks and two H&M tracks, and one freight track.
There were two Pennsy passenger tracks from Manhattan Transfer to Jersey City, one eastward, one westward. They used the outer side of each MT platform. The Pennsy tracks to and from NY usually used the inner side of each MT platform.
There would normally be a need to get the westward track (JC to MT) and both H&M tracks through the NY embankment. The eastward MT to JC track would already be properly aligned relative to the embankment.
I suspect there was also a fright track for trains from Meadows to access the Center Street branch, the First Street freight house in Harrison, etc. H&M, of course, had to be on the north side to access the river and Newark's Saybrook Streeet / Park Place station.
At first, I though the PSCT #43 trolley line might also need an opening, but it remained on the north side of Harrison Ave and had its own underpass of the High Line near the current location of the USPS and Harrison Ave.