nL-n-Luc5b   nL-Ref/Par2-Construction 

nL-n-Luc5b is a Level-up construction which uses the Reference n-Line Ref and the 2nd generation parallel n-Line Par2 wrt some lower-level center to construct a Perspective / Homothetic Center. See nL-n-Luc5.
When Par1 is homothetic with Ref, consequently also Par2 will be homothetic with Par1. We have actually a Ref/Par1/Par2 relationship. However it is possible that Par1 is not homothetic or even perspective with Ref, whilst Par2 still is.
There are no examples of this level-up construction found yet, but in principle their existence should be possible.