Vibration suppression capabilities of linear passive vibration absorbers, such as traditional tuned mass damper (TMD), and recently proposed inerter-based vibration absorbers, have been studied for multiple mechanical systems. In particular, significant performance advantages have been obtained with a specific device making use of both inerter and mass elements, namely the tuned mass damper inerter (TMDI). However, there are still countless mass-included inerter-based configurations that have not been studied, which can potentially provide more preferred dynamic properties. In this paper, an immittance-function-layout (IFL) is introduced, which can cover a large range of topological connection possibilities with both mass and inerter elements. With the recently proposed structural immittance format, a systematic approach is established to identify the most beneficial IFL type mass-included inerter-based configurations with pre-determined number of each element type. Vibration suppression performance with single-IFL type device and two parallel-connected IFLs (i.e. dual-IFL) type devices are investigated in this paper. Three optimal configurations are identified for mitigating the maximum inter-storey drift of an example 3-storey building model subjected to base excitation. With this 3-storey building model, results show that, for the optimum single-IFL configuration, the performance improvement is 7.3% compared with the optimum TMDI, and with identified beneficial dual-IFL configurations, up to 34.9% performance advantages are obtained. Furthermore, consistent performance gains are shown under real-life earthquake inputs and with a 10-storey building model using identified absorber configurations.