The low energy excited 0 + 2,3 states in 96 Sr are amongst the most prominent examples of shape coexistence across the nuclear landscape. In this work, the neutron [2s 1/2 ] 2 content of the 0 + 1,2,3 states in 96 Sr was determined by means of the d( 95 Sr,p) transfer reaction at the TRIUMF-ISAC2 facility using the SHARC and TIGRESS arrays. Spectroscopic factors of 0.19(3) and 0.22 (3) were extracted for the 96 Sr ground and 1229 keV 0 + states, respectively, by fitting the experimental angular distributions to DWBA reaction model calculations. A detailed analysis of the γ-decay of the isomeric 0 + 3 state was used to determine a spectroscopic factor of 0.33(13). The experimental results are compared to shell model calculations, which predict negligible spectroscopic strength for the excited 0 + states in 96 Sr. The strengths of the excited 0 + 2,3 states were also analyzed within a two-level mixing model and are consistent with a mixing strength of a 2 =0.40(14) and a difference in intrinsic deformations of |∆β| = 0.31(3). These results suggest coexistence of three different configurations in 96 Sr and strong shape mixing of the two excited 0 + states.