An extended reaction kinetics model (RKM) suitable for the analysis of weakly ionised, non-thermal argon plasmas with gas temperatures around 300 K at sub-atmospheric and atmospheric pressures is presented. It considers 23 different species including electrons as well as the ground state atom, an atomic and molecular ion, four excited molecular states, and 15 excited atomic states of argon, where all individual 1s and 2p states (in Paschen notation) are included as a separate species. This 23-species RKM involves 409 collision processes and radiative transitions and recent electron collision cross section data. It is evaluated by means of results of time- and space-dependent fluid modelling of argon discharges and their comparison with measured data for two different dielectric barrier discharge configurations as well as a micro-scaled atmospheric-pressure plasma jet setup. The results are also compared with those obtained by use of a previously established 15-species RKM involving only the two lumped 2p states 2p10…5 and . It is found that the 23-species RKM shows generally better agreement with experimental data and provides more options for direct comparison with measurements than the frequently used 15-species RKM.