  In this work, we explore the twist operator OPEs of a generic bosonic
symmetric product ($S_N$) orbifold CFT. We conjecture that at large $N$ the OPE
of bare twist operators contains only bare twists and excitations of bare
twists with fractional Virasoro modes. These fractionally excited operators are
the only ones that depend exclusively on the lengths of the twists and the
central charge, agreeing with the general structure of correlators of bare
twists found in the literature. To provide evidence for this, we study the
coincidence limit of a four point function of bare twist operators to several
non-leading orders. We show how the coefficients of these powers can be
reproduced by considering bare twist operators excited by fractional Virasoro
modes in the exchange channels.
