  Constraints on gravity and cosmology will greatly benefit from performing
joint clustering and weak lensing analyses on large-scale structure data sets.
Utilising non-linear information coming from small physical scales can greatly
enhance these constraints. At the heart of these analyses is the matter power
spectrum. Here we employ a simple method, dubbed "Hybrid $P_\ell(k)$", based on
the Gaussian Streaming Model (GSM), to calculate the quasi non-linear redshift
space matter power spectrum multipoles. This employs a fully non-linear and
theoretically general prescription for the matter power spectrum. We test this
approach against comoving Lagrangian acceleration simulation measurements
performed in GR, DGP and $f(R)$ gravity and find that our method performs
comparably or better to the dark matter TNS redshift space power spectrum model
for dark matter. When comparing the redshift space multipoles for halos, we
find that the Gaussian approximation of the GSM with a linear bias and a free
stochastic term, $N$, is competitive to the TNS model. Our approach offers many
avenues for improvement in accuracy as well as further unification under the
halo model.
