In the extended scalar sector of the SMASH (Standard Model - Axion - Seesaw - Higgs portal inflation) framework, we conduct a phenomenological investigation of the observable effects. In a suitable region of the SMASH scalar parameter spaces, we resolve the vacuum metastability issue and discuss the one-loop correction to the triple Higgs coupling λHHH. The λHHH and SM Higgs quartic coupling λH corrections are found to be proportional to the threshold correction. A large λHHH correction (≳5%) implies vacuum instability in the model and thus limits the general class of theories that use threshold correction. We perform a full two-loop renormalization group analysis of the SMASH model.