The diagonalization manifold in similarity transformed equation-of-motion coupled cluster (STEOM-CC) theory is extended to include doubly excited determinants. In the resulting extended-STEOM approach accurate results are obtained for doubly excited states in small model systems for which full configuration interaction (CI) benchmark results are available (similar to 0.1 eV errors). On the other hand, extended-STEOM results are found to be virtually identical (< 0.1 eV shifts) to the original STEOM results for states that are dominated by single excitations, at least in prototypical organic molecules. The extended-STEOM method is also applied to the transition metal complexes TiCl4, Ni(CO)(4), and MnO4-, and yields improved results compared to STEOM and EOM-CCSD. For highly correlated systems, like the permangenate anion, results are not yet fully satisfactory however. In these cases the dominant source of error appears to be the description of ground, ionized, and attached states that underly the similarity transformed Hamiltonian in the extended-STEOM approach.