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We study two families of composite twisted Ramond fields (made by products oftwo operators) in the $\cal {N}=(4,4)$ supersymmetric D1-D5 SCFT$_2$ deformedby a marginal modulus operator away from its $(T^4)^N/ S_N$ free orbifoldpoint. We construct the large-$N$ contributions to the four-point functionswith two composite operators and two deformation fields. These functions allowus to derive short-distance OPE limits and to calculate the anomalousdimensions of the composite operators. We demonstrate that one can distinguishtwo sets of composite Ramond states with twists $m_1$ and $m_2$: protectedstates, for which $m_1+m_2=N$, and "lifted" states for which $m_1+m_2<N$. Thelatter require an appropriate renormalisation. We also derive the leading ordercorrections to their two-point functions, and to their three-point functionswith the deformation operator.

Correlation functions of composite Ramond fields in deformed D1-D5 orbifold SCFT$_2$