We present the first application of a ‘ multiple-tracer ’ redshift-space distortion ( RSD ) analysis to an observational galaxy sample , using data from the Galaxy and Mass Assembly survey ( GAMA ) . Our dataset is an r < 19.8 magnitude-limited sample of 178 { , } 579 galaxies covering redshift interval z < 0.5 and area 180 deg ^ { 2 } . We obtain improvements of 10 - 20 \% in measurements of the gravitational growth rate compared to a single-tracer analysis , deriving from the correlated sample variance imprinted in the distributions of the overlapping galaxy populations . We present new expressions for the covariances between the auto-power and cross-power spectra of galaxy samples that are valid for a general survey selection function and weighting scheme . We find no evidence for a systematic dependence of the measured growth rate on the galaxy tracer used , justifying the RSD modelling assumptions , and validate our results using mock catalogues from N-body simulations . For multiple tracers selected by galaxy colour , we measure normalized growth rates in two independent redshift bins f \sigma _ { 8 } ( z = 0.18 ) = 0.36 \pm 0.09 and f \sigma _ { 8 } ( z = 0.38 ) = 0.44 \pm 0.06 , in agreement with standard GR gravity and other galaxy surveys at similar redshifts .