From what I read, the tracks of both levels of the Parson-archer station continues east towards 160th Street and South Road. The upper level tracks are unique cause there are provisions for a portal for the tracks to rise up and merge with the nearby LIRR ROW at 158th Street. Was it to capture that line or to create some kind of hybrid service?
Looking on Google Maps at 160th Street and South Road, there is a football field and tennis courts in that vicinity, and unless I'm looking wrong, I'm not sure if there's even room for a tunnel portal without bulldozing that area.
Here's a picture of the so called upper level layup track I found online.
http://www.nycsubway.org/perl/show?107334
In the future, if the MTA decides to extend the Archer Avenue Line, will it follow the original plans of the Program for Action of 1968, where it would rise from a portal at that location to link with the LIRR line? Is that even possible in this day of age?