  We extend our previous redshift space power spectrum code to the redshift
space correlation function. Here we focus on the Gaussian Streaming Model
(GSM). Again, the code accommodates a wide range of modified gravity and dark
energy models. For the non-linear real space correlation function used in the
GSM, we use the Fourier transform of the RegPT 1-loop matter power spectrum. We
compare predictions of the GSM for a Vainshtein screened and Chameleon screened
model as well as GR. These predictions are compared to the Fourier transform of
the Taruya, Nishimichi and Saito (TNS) redshift space power spectrum model
which is fit to N-Body data. We find very good agreement between the Fourier
transform of the TNS model and the GSM predictions, with $\leq 6\%$ deviations
in the first two correlation function multipoles for all models for separations
in $50$Mpc$/h \leq s \leq 180$Mpc/$h$. Excellent agreement is found in the
differences between the modified gravity and GR multipole predictions for both
approaches to the redshift space correlation function, highlighting their
matched ability in picking up deviations from GR. We elucidate the timeliness
of such non-standard templates at the dawn of stage-IV surveys and discuss
necessary preparations and extensions needed for upcoming high quality data.
