  We consider correlation functions in symmetric product ($S_N$) orbifold CFTs
at large $N$ with arbitrary seed CFT, expanding on our earlier work
arXiv:2211.04633 . Using covering space techniques, we calculate descent
relations using fractional Virasoro generators in correlators, writing
correlators of descendants in terms of correlators of ancestors. We first
consider the case three-point functions of the form
($m$-cycle)-($n$-cycle)-($q$-cycle) which lift to arbitrary primaries on the
cover, and descendants thereof. In these examples we show that the final
descent relations do not depend on the covering space data, nor on the specific
details of the seed CFT. This makes these descent relations universal in all
$S_N$ orbifold CFTs. Next, we explore four-point functions of the form
(2-cycle)-($n$-cycle)-($n$-cycle)-(2-cycle) which lift to arbitrary primaries
on the cover, and descendants thereof. In such cases a single parameter in the
map $s$ parameterizes both the base space cross ratio $\zeta_z$ and the
covering space cross ratio $\zeta_t$. We find that the descent relations for
the four point functions depend only on base space data and the parameter $s$,
which we argue is tantamount to writing the descent relations in terms of the
base space data and the base space cross ratio. These descent relations again
do not depend on the covering space data, nor the specifics of the seed CFT,
making these universal as well.
