Inclusion Criteria:

          -  Male or female, ≥18 years old with the ability to understand and provide signed and
             witnessed informed consent, and agree to comply with protocol requirements

          -  Part A: Participants must have one of the histologically-confirmed solid malignancies
             listed below, must be clinically disease-free at study entry (that is, participants in
             the adjuvant setting). Participants will be permitted to complete any standard of care
             adjuvant therapy prior to study entry, and those not eligible for any standard of care
             adjuvant treatment or who decline such treatment are permitted to consent to this
             study, as long as all treatment options have been transparently disclosed and
             documented in the participant's medical record.

          -  Part B: Participants must have one of the histologically- or cytologically-confirmed
             unresectable (locally advanced or metastatic) solid malignancies listed below, have
             measurable disease at study entry defined by Response Evaluation Criteria in Solid
             Tumors (RECIST) Version 1.1., and be considered suitable for treatment with
             pembrolizumab; in this study pembrolizumab will be considered an investigational study
             drug.

        Participants with any of the following solid malignancies:

        a. Non-small cell lung cancer (participants in Part B must either lack epidermal growth
        factor receptor (EGFR) sensitizing mutation or anaplastic lymphoma kinase (ALK)
        translocation per local test results or must have progressed on approved standard of care
        treatment for EGFR or ALK positive non-small cell lung cancer [NSCLC]) b. Small cell lung
        cancer c. Melanoma d. Bladder urothelial carcinoma e. Human papillomavirus-negative head
        and neck squamous cell carcinoma (HPV-ve HNSCC) f. Any solid malignancy known to be
        microsatellite instable (MSI) high/mismatch repair (MMR) deficient g. Any solid malignancy
        known to have a high tumor mutational load/burden

          -  Part C: Participants must have one of the histologically- or cytologically confirmed
             unresectable (locally advanced or metastatic) solid malignancies listed below, must
             not have received prior anti-programmed cell death protein 1 (PD-1)/programmed death
             -ligand 1 (PD-L1) therapy, and must have measurable disease at study entry defined by
             RECIST 1.1.

               1. Microsatellite stable (MSS)-CRC

               2. HPV-ve metastatic or recurrent HPV-ve HNSCC of the oral cavity, oropharynx,
                  hypopharynx, or larynx

               3. Bladder urothelial carcinoma

          -  Part D: Participants must have completed resected adjuvant melanoma and must be
             clinically disease-free at study entry. Participants will be permitted to complete any
             standard of care adjuvant therapy prior to study entry, and those not eligible for any
             standard of care adjuvant treatment or who decline such treatment are permitted to
             consent to this study, as long as all treatment options have been transparently
             disclosed and documented in the participant's medical record.

          -  Parts A and D: Participants must have a formalin-fixed paraffin embedded (FFPE) tumor
             sample available (for example, from their prior surgery) that is suitable for the next
             generation sequencing (NGS) required for this study.

          -  Parts B and C: Participants must have at least 1 lesion amenable to the mandatory
             fresh tumor biopsy at study entry and provide a biopsy suitable for the next
             generation sequencing (NGS) required for this study. An existing (archival) FFPE tumor
             sample may instead be used for NGS after discussing with medical monitor.

          -  Participants must have resolution of toxic effect(s) from prior therapy to Grade 1 or
             less. Participants with Grade ≤2 neuropathy or alopecia are an exception to this
             criterion. If a participant received major surgery or radiation therapy of >30 gray
             (Gy), they must have recovered from the toxicity and/or complications from the
             intervention to Grade 1 or less.

          -  Participant is willing to use an adequate method of contraception for the course of
             the study through 120 days after the last dose of study drug (male and female
             participants of childbearing potential).

          -  Participants with Performance Scale (PS) of 0 or 1 on the Eastern Cooperative Oncology
             Group (ECOG) PS

          -  Life expectancy >12 weeks at Screening

          -  Participants with adequate organ and marrow function

          -  Parts A and D: Participant must consent to required apheresis procedure and meet
             additional inclusion criteria per local institutional apheresis procedure.

        Exclusion Criteria:

          -  Treatment with any of the following:

               1. Any investigational agents, anti-cancer monoclonal antibody, anti-cancer
                  therapeutic vaccine, immunostimulant (for example, IL-2), or study drugs from a
                  previous clinical study within 4 weeks of the first dose of mRNA-4157 or
                  pembrolizumab (note only a 2 week wash out is required from prior pembrolizumab
                  treatment)

               2. Any chemotherapy, targeted small molecule therapy, or radiation therapy within 2
                  weeks of the first dose of mRNA-4157 or pembrolizumab

               3. Live-virus vaccination within 30 days of the first dose of mRNA-4157 or
                  pembrolizumab. Seasonal flu vaccines that do not contain live virus are
                  permitted.

               4. Any systemic steroid therapy or other form of immunosuppressive therapy within 7
                  days of the first dose of mRNA-4157 or pembrolizumab

               5. Transfusion of blood products (including platelets or red blood cells [RBCs]) or
                  administration of colony stimulating factors (including granulocyte colony
                  stimulating factor [G-CSF], granulocyte/macrophage colony stimulating factor
                  [GM-CSF], or recombinant erythropoietin) within 1 week of the NGS blood sample
                  during screening, and 4 weeks of the first dose of mRNA-4157 or pembrolizumab

          -  Prior PD-1/PD-L1 treatment is permitted for participants in Parts A, B, and D of this
             study, but only participants who have progressed on their prior PD-1/PD-L1 treatment
             without a partial or complete response, and without discontinuing for drug-related
             toxicity are eligible.

          -  Active central nervous system metastases and/or carcinomatous meningitis

          -  Active autoimmune disease that has required systemic treatment in past 2 years

          -  Has a history of (noninfectious) pneumonitis that required steroids or has current
             pneumonitis

          -  Has a diagnosis of immunodeficiency

          -  Any clinically-significant cardiac disease defined as New York Heart Association Class
             III or IV within the past 6 months of Screening, unless, in the opinion of the
             Investigator, the disease is well-controlled

          -  A history or current evidence of any condition, therapy, or laboratory abnormality
             that might confound the results of the study, interfere with participation for the
             full duration of the study, or is not in the best interest of the participant to
             participate, in the opinion of the treating Investigator

          -  Known psychiatric or substance abuse disorders that would interfere with cooperation
             with the requirements of the trial

          -  Previously identified hypersensitivity to components of the formulations used in this
             study

          -  Had a solid organ or allogeneic bone marrow transplant

          -  Participants with a history of interstitial lung disease

          -  An active infection requiring systemic therapy

          -  A known history of human immunodeficiency virus (HIV)

          -  Known active Hepatitis B or Hepatitis C

          -  Known additional malignancy that is progressing or requires active treatment,
             exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the
             skin that has undergone curative therapy, or in situ cervical cancer

          -  Participants participating in apheresis; mandatory in the Part A apheresis expansion
             phase cohort and Part D (optional for other study parts), must not meet any of the
             exclusion criteria on any day when apheresis is performed, either protocol specific
             apheresis criteria, or per local institutional apheresis protocol.