Fréchet  regression  model  (Peterson  &  Müller  2019)  provides  a  promising framework  for  regression  analysis  with  metric  space-valued  responses,  which are frequently encountered in new statistical applications.  However, as in the classical setting, regression accuracy drops significantly as the dimension of the predictor  becomes  large.   We  propose  a  novel  sufficient  dimension  reduction (SDR)  framework  for  Fréchet  regression  models,  which  can  turn  any  existing SDR method for Euclidean (X, Y) into one for Euclidean X and metric space-valued Y.  Specifically,  we map the statistical object to a real-valued random variable by a family of functions, which we call an ensemble, and perform classical SDR on the transformed Y. We show that, when the family of transformations is rich enough, we can assemble the results for transformed responses to fully recover the Fréchet SDR space.  The finite sample performance of the methods is illustrated through simulation studies for several special cases that include  Wasserstein  space,  the  space  of  symmetric  positive  definite  matrices and the sphere.  The SDR for Fréchet regression can also be used to assist data visualization.  This is illustrated for human mortality data.