The purpose of this study is to assess the safety and tolerability of mRNA-4106 monotherapy and of mRNA-4200 in combination with checkpoint inhibitor therapy in participants with solid tumors.

Key Inclusion Criteria:

• Arm 1: Histologically confirmed advanced or metastatic cancer (melanoma, non-small cell lung cancer (NSCLC), hepatocellular carcinoma (HCC), esophageal carcinoma, head and neck squamous cell carcinoma (HNSCC), urinary bladder cancer (UBC), colon/rectal adenocarcinomas, gastric, ovarian, cervical, and endometrial carcinomas) with measurable disease as determined by Response Evaluation Criteria In Solid Tumors volume 1.1 (RECIST v1.1) and have completed or refused all standard therapies (no limit to prior lines of therapy). Participants must have a tumor lesion amenable to biopsy, or alternatively archival tumor tissue is acceptable as long as the collection date is within one year of the enrollment date.
• Arm 2: Histologically confirmed advanced or metastatic cancer (melanoma, NSCLC, esophageal carcinoma, HNSCC, urothelial/bladder carcinoma, gastric, colon/rectal adenocarcinomas, ovarian, cervical, and endometrial carcinomas [Note: HCC not included]) with measurable disease as determined by RECIST v1.1 and have completed or refused all standard therapies (no more than 5 prior lines of therapy). Participants must have a tumor lesion amenable to biopsy, or alternatively archival tumor tissue is acceptable if no intervening systemic therapy was received.
• Arm 2: Participant life expectancy of ≥90 days.
• Arm 1 and Arm 2: Participant has an Eastern Cooperative Oncology Group performance status of ≤1.
• Arm 1 and Arm 2: Participant has adequate hematological and biological function.
• Arm 1 and Arm 2: Participants who could become pregnant: negative pregnancy test within 24 hours before the first dose of study treatment.

Key Exclusion Criteria:

• Arm 1 and Arm 2: Participant has active central nervous system tumors or metastases
• Arm 1 and Arm 2: Participant has received treatment with prohibited medications/treatments (that is, concurrent anticancer therapy including other chemotherapy, hormonal anticancer therapy, biologic therapy, or immunotherapy) or investigational agents within 5 half-lives or 14 days prior to the first day of study treatment (Cycle 1 Day 1), whichever is shorter.
• Arm 1 and Arm 2: Participant has required the use of immunosuppressive doses of systemic steroids or absorbed topical steroids (doses >10 milligrams [mg] prednisone daily equivalent) within 2 weeks before study treatment administration or currently requiring maintenance doses of >10 mg prednisone or equivalent per day.
• Arm 1 and Arm 2: Participant has any plan to receive a live attenuated vaccine during study treatment or has received a live vaccine within 30 days before the first dose of study treatment.
• Arm 1 and Arm 2: Participant has reversible toxicities from prior cancer therapy that have not recovered to Grade 1 or baseline. Any unresolved toxicity National Cancer Institute Common Terminology Criteria for Adverse Events Grade ≥2 from previous anticancer therapy with the exception of alopecia, vitiligo, and prespecified laboratory values.
• Arm 1 and Arm 2: Participant has any unstable or clinically significant concurrent medical/psychiatric illness or social situation that would limit compliance with study requirements or compromise the ability of the participant to provide written informed consent, per the discretion of the Investigator.
• Arm 1 and Arm 2: Participant has concurrent enrollment in another clinical study (unless it is an observational noninterventional clinical study).

Note: Other inclusion and exclusion criteria may apply.