This paper provides a comprehensive analysis of local and concurrent commutation failure (CF) of multi-infeed high-voltage direct current (HVDC) system considering multi-infeed interaction factor (MIIF). The literature indicates that the local CF is not influenced by MIIF, whereas this paper concludes that both the local CF and concurrent CF are influenced by MIIF. The ability of remote converter to work under reduced reactive power enables its feature to support local converter via inter-connection link. The MIIF measures the strength of electrical connectivity between converters. Higher MIIF gives a clearer path to remote converter to support local converter, but at the same time, it provides an easy path to local converter to disturb remote converter under local fault. The presence of nearby converter increases the local commutation failure immunity index (CFII) while reducing concurrent CFII. Higher MIIF causes reactive power support to flow from remote converter to local converter, which reduces the chances of CF. A mathematical approximation to calculate the increase in local CFII for multi-infeed HVDC configurations is also proposed. A power flow approach is used to model the relation between MIIF and reactive power support from remote end. The local and concurrent CFIIs are found to be inverse to each other over MIIF; therefore, it is recommended that there is an optimal value of MIIF for all converters in close electric proximity to maintain CFII at a certain level. The numerical results of established model are compared with PSCAD/EMTDC simulations. The simulation results show the details of the influence of MIIF on local CF and concurrent CF of multi-infeed HVDC, which validates the analysis presented.