The interaction between the receptor-binding domain of the SARS-CoV-2 spike glycoprotein and the ACE2 enzyme is believed to be the entry point of the virus into various cells in the body, including the lungs, heart, liver, and kidneys. The current focus of several therapeutic design efforts explore attempts at affecting the binding interaction between the two proteins to limit the activity of the virus and disease progression. In this work, we analyze the stability of the spike protein under all possible single-point mutations in the receptor-binding domain and computationally explore mutations that can affect the binding with the ACE2 enzyme. We unravel the mutation landscape of the receptor region and assess the toxicity potential of single and multi-point mutations, generating insights for future vaccine efforts on potential mutations that might further stabilize the spike protein and increase its infectivity. We developed a tool, called SpikeMutator, to construct full atomic protein structures of the mutant spike proteins and shared a database of 3,800 single-point mutant structures. We analyzed the recent 65,000 reported spike sequences across the globe and observed the emergence of stable multi-point mutant structures. Using the landscape, we searched through 7.5 million possible 2-point mutation combinations and report that the (R355D K424E) mutation produces one of the strongest spike proteins that therapeutic efforts should investigate for the sake of developing an effective vaccine.