We report ionization cross section measurements for electron impact single ionization (EISI) of Fe11+ forming Fe12+ and electron impact double ionization (EIDI) of Fe11+ forming Fe13+. The measurements cover the center-of-mass energy range from approximately 230 eV to 2300 eV. The experiment was performed using the heavy-ion storage ring TSR located at the Max-Planck-Institut für Kernphysik in Heidelberg, Germany. The storage ring approach allows nearly all metastable levels to relax to the ground state before data collection begins. We find that the cross section for single ionization is 30% smaller than was previously measured in a single-pass experiment using an ion beam with an unknown metastable fraction. We also find some significant differences between our experimental cross section for single ionization and recent distorted wave (DW) calculations. The DW Maxwellian EISI rate coefficient for Fe11+ forming Fe12+ may be underestimated by as much as 25% at temperatures for which Fe11+ is abundant in collisional ionization equilibrium. This is likely due to the absence of 3s excitation-autoionization (EA) in the calculations. However, a precise measurement of the cross section due to this EA channel was not possible because this process is not distinguishable experimentally from electron impact excitation of an n = 3 electron to levels of n ≥ 44 followed by field ionization in the charge state analyzer after the interaction region. Our experimental results also indicate that the EIDI cross section is dominated by the indirect process in which direct single ionization of an inner shell 2l electron is followed by autoionization, resulting in a net double ionization.