This work investigates the effects of fuel and oxidizer flexibility on the operability of a partially premixed combustor stabilizing H-2-enriched compressed natural gas (CNG) oxy-flames over a perforated plate burner. Three sets of experiments were conducted over ranges of equivalence ratio (Phi), oxygen fraction (OF), and hydrogen fraction (HF). The first set was performed at OF = 29% to investigate the effects of H-2 addition (HFs: 0.0%, 10%, 20%, and 30%) on the combustor operability and flame macrostructure over ranges of (I) and inlet flow Reynolds (Re). In the second set, the experiments of the first set were repeated for different OFs (29%, 32%, and 36%) to study the effects of oxidizer flexibility on combustor operability and visual flame appearance. In the last set, the combustor operability was examined near stoichiometry (Phi = 0.85) over ranges of OF, HF, and Re. At Re = 1481 and OF = 29%, the lean blowout limit was extended from Phi of 0.55 for HF of 0.0% to Phi of 0.38, 0.35, and 0.30 for HFs of 10%, 20%, and 30%, respectively. However, the flashback limit was narrowed with H2 addition at Re = 1481 and OF = 32% from Phi = 1.1 for HF = 0.0 to Phi = 1.05 and 1.0 for HF of 20% and 30%, respectively. The flame becomes whiter, shorter, more intense within the inner cone and more stable with strong attachment to the plate with H-2 addition. Flames of similar Phi and OF, i.e., similar adiabatic flame temperature (T-ad), resulted in similar flame shape. The operability of the combustor near stoichiometry (Phi = 0.85) was not possible outside the range of OF from 25% (at blowout) to 46% (at flashback). The lean blowout limit of the combustor near stoichiometry was extended to lower OFs with H-2 addition. The combustor was able to drop down with the OF from 28% to 25% when the HF was raised from 0.0% to 30% at Phi = 0.85 and Re of 1481. However, it is advised to keep OF below 36% at HF of 30% to avoid flame flashback. The results showed that the flow Re becomes the dominant parameter controlling the combustor blowout limit, and reaction kinetics rates dominate the control of the flashback limit. Having similar inlet flow characteristics, i.e., at fixed Re, T(ad )becomes the most relevant parameter choice when designing a combustion system in order to avoid flame flashback when operated at medium to full load conditions whatever the flame type (partially or fully premixed flames) whatever the stabilization mechanism (swirl or perforated plate).