  Let $\mathcal{G}^*(S,\rho)$ be the graph whose vertices are marked complex
projective structures with holonomy $\rho$ and whose edges are graftings from
one vertex to another. If $\rho$ is quasi-Fuchsian, a theorem of Goldman
implies that $\mathcal{G}^*(S,\rho)$ is connected. If $\rho(\pi_1(S))$ is a
Schottky group Baba has shown that $\mathcal{G}(S,\rho)$ (the corresponding
graph for unmarked structures) is connected. For the case that $\rho(\pi_1(S))$
is a Schottky group, this paper provides formulae for the composition of
graftings in a basic setting. Using these formulae, one can construct an
infinite number of (standard) projective structures which can be grafted to a
common structure. Furthermore, one can construct pairs of projective structures
which can be connected by grafting in an infinite number of ways.
