The injection of hydrogen into the natural gas network can contribute to the large-scale integration of renewables, as hydrogen can be easily produced through electrolysis from wind or solar energy. However, the addition of hydrogen to natural gas influences fuel properties, asking for the assessment of the safe and efficient operation of existing end-user equipment, such as domestic burners and boilers. In this work, 3-dimensional resolved numerical simulations based on Computational Fluid Dynamics are carried out to shed light on the effect of H2 addition on the combustion process occurring in condensing boilers equipped with perforated cylindrical burners. To this purpose, multi-hole geometries emulating a portion of a perforated burner are analyzed. Since the burner holes are positioned very close to each other, the interaction of the adjacent laminar premixed flames is observed to occur with influence on the flow and thermo-chemical fields which differ from those of a single premixed flame. The addition of hydrogen was found to lead to an anticipation of the reaction zone, although the general features observed with the G222 gas (23% H2, 77% CH4 ) were alike those of the G20 gas (100% CH4).