SARS-CoV-2 variants have evolved over time in recent years, demonstrating immune evasion of vaccine-induced neutralizing antibodies directed against the original S protein. Updated S-targeted vaccines provide a high level of protection against circulating variants of SARS-CoV-2, but this protection declines over time due to ongoing virus evolution. To achieve a broader protection, novel vaccine candidates involving additional antigens with low mutation rates are currently needed. Based on our recently studied mRNA lipid nanoparticle (mRNA-LNP) platform, we have generated mRNA-LNP encoding SARS-CoV-2 structural proteins M, N, S from different virus variants and studied their immunogenicity separately or in combination in vivo. As a result, all mRNA-LNP vaccine compositions encoding the S and N proteins induced excellent titers of RBD- and N-specific binding antibodies. The T cell responses were mainly specific CD4+ T cell lymphocytes producing IL-2 and TNF-alpha. mRNA-LNP encoding the M protein did not show a high immunogenicity. High neutralizing activity was detected in the sera of mice vaccinated with mRNA-LNP encoding S protein (alone or in combinations) against closely related strains, but was undetectable or significantly lower against an evolutionarily distant variant. Our data showed that the addition of mRNAs encoding S and M antigens to mRNA-N in the vaccine composition enhanced the immunogenicity of mRNA-N and induced a more robust immune response to the N protein. Based on our results, we suggested that the S protein plays a key role in enhancing the immune response to the N protein when they are both encoded in the mRNA-LNP vaccine.