Thermoacoustic instabilities in combustion systems are influenced by the thermoacoustic properties, such as the transfer function (TF) of the burner with flame. One promising approach to address these instabilities is by targeting the burner's thermoacoustic properties. The approach developed in this contribution is based on an idea of modifying or designing a targeted composite flame transfer function (TF) and involves the heuristic concept that the acoustic response of a particular flame can be counterbalanced by the corresponding response of other flames. For premixed conical flames anchored on the burner deck, at the fixed gas composition the TF mostly depends on such parameters as the diameter of the perforations and the flame spacing (pitch). This suggests the concept of combining different sizes and shapes of perforations in one burner deck. In this study, we investigate the acoustic response of burners made of sintered ceramic fibers with multiple patterns of perforation using the TF composition strategy. This approach allows us to represent the cumulative flame TF as a weighted sum of the elemental TF of the flame groups, based on the additive nature of the individual heat release rate of the flames. We first show how this approach can be used to design composite burners that operate thermo-acoustically stable in a given system. Then, we mark the critical frequency range for the designed composite burners in the frequency domain using the so-called direct conservative stability (DCS) criterion. Following this, a stability map representing the complete picture of safe values of gain and phase of the flame TF is introduced that can serve as a designing target. Finally, we use stability margin and uncertainty analysis based on Monte-Carlo simulation to check the robustness of designed composite burner. Novelty and significance statement center dot We have introduced a systematic flame stabilization framework centered around flame modification. center dot This framework allows for the utilization of various characterized basic/elemental burners, each with their associated flames, to design complex burners capable of achieving thermoacoustic stability. center dot Leveraging the DCS framework for stability analysis, we have generated a comprehensive stability map for the thermoacoustic system. This map provides a design target and guidance for systematic flame stabilization. center dot Recognizing the presence of uncertainties in the simulation and measurement of subsystems (including upstream and downstream reflection coefficients and flame transfer functions), we have demonstrated that stability margin can serve as a robustness indicator for the design. We have included the minimum acceptable stability margin along with uncertainties in the stability map, making it a valuable tool for assessing robustness in burner development within the context of thermoacoustics. center dot A pressure drop composition model, designed to estimate the pressure drop of a complex burner based on the pressure drop of its individual segments, has been proposed and tested. center dot We have introduced the concept of flame transfer function composition for segmented/partitioned burners, which has been proposed, validated, and elaborated upon for designing intricate industrial composite burners.