Inclusion Criteria:

        For Dose Escalation Phase:

          -  Have any histologically- or cytologically-confirmed advanced/metastatic solid tumor
             (except NSCLC for Cohorts 2 and 3) by pathology report and have received, been
             intolerant to, been ineligible for, or refused all treatment known to confer clinical
             benefit

        For Dose Confirmation Phase NSCLC Arms (A, B, C, and E):

          -  Have newly diagnosed histologically or cytologically-confirmed stage IIIB/stage IV
             NSCLC. Epidermal growth factor receptor (EGFR)-and anaplastic lymphoma kinase (ALK)
             translocation-directed therapy is not indicated as primary therapy. Participant must
             not have received prior systemic treatment for advanced NSCLC or must have received
             previous neoadjuvant and adjuvant chemotherapies ≥6 months before dosing of study drug
             if prior systemic treatment was given for early stage disease

        For Dose Confirmation Phase SCLC Arm (Arm D):

          -  Have histologically- or cytologically-confirmed metastatic (Stage III/IV) SCLC with
             progressive disease after ≥1 platinum-based chemotherapy regimen. Participants with
             platinum-sensitive disease are eligible

          -  Have measurable disease by RECIST 1.1 as assessed by the local site
             investigator/radiology

          -  Have Eastern Cooperative Oncology Group (ECOG) Performance Scale status of 0 or 1

          -  A female participant is eligible to participate if she is not pregnant or
             breastfeeding and at least 1 of the following conditions applies:

          -  Is not a woman of child bearing potential (WOCBP) OR

          -  Is a WOCBP and using a contraceptive method that is highly effective during the
             intervention period and for at least 120 days after the last dose of pembrolizumab or
             pembrolizumab/quavonlimab, whichever comes last

          -  Female participants of childbearing potential must have negative urine or serum
             pregnancy test within 24 hours for urine and within 72 hours for serum prior to
             receiving the first dose of study treatment

          -  Male participants with a female partner(s) of child-bearing potential must be willing
             to use an adequate method of contraception for the course of the study through 120
             days after the last dose of study medication and refrain from donating sperm during
             this period

          -  Must submit an evaluable baseline tumor sample for analysis (either a recent or
             archival tumor sample)

        For Efficacy Expansion Phase Arms F and G and Coformulation Phase Arm J:

          -  Have histologically/cytologically-confirmed unresectable Stage III or Stage IV
             melanoma per American Joint Committee on Cancer (AJCC) staging system version 8, not
             amenable to local therapy

          -  Have at least 1 measurable lesion by CT or MRI per RECIST 1.1 by BICR. Cutaneous
             lesions and other superficial lesions are not considered measurable lesions for the
             purposes of this protocol, but may be considered as non-target lesions

          -  Participants with unresectable Stage III or IV disease must have progressed on
             treatment with an anti-PD-1/L1 monoclonal antibody (mAb) administered either as
             monotherapy, or in combination with other checkpoint inhibitors or other therapies
             (combinations with anti-cytotoxic T-lymphocyte associated protein 4 [CTLA-4] agents
             will not be allowed)

          -  Participants who receive anti-PD-1 therapy as adjuvant treatment following complete
             resection of Stage III or IV melanoma and have disease recurrence (unresectable
             loco-regional disease or distant metastases) while on active treatment or within 6
             months of stopping anti-PD-1 are eligible

          -  Have submitted pre-trial imaging and provided a baseline tumor sample

          -  Proto-oncogene B-raf (BRAF) V600 mutation-positive melanoma participants should have
             received targeted therapy for advanced or metastatic disease (eg, BRAF/MEK inhibitor,
             alone or in combination) prior to enrolling on this study; however, they are not
             required to progress on this treatment prior to enrollment

          -  BRAF V600E mutation-positive melanoma participants who have NOT received a BRAF
             inhibitor (either as adjuvant therapy or in the metastatic disease setting) with
             lactate dehydrogenase (LDH) < local upper limit of normal (ULN), no clinically
             significant tumor-related symptoms, and absence of rapidly progressing metastatic
             melanoma. Approximately 10 participants each from Arms F, G, and J will have 2
             mandatory biopsies

        For Dose Coformulation Phase Arm I:

          -  Have any histologically- or cytologically-confirmed advanced/metastatic solid tumor by
             pathology report and have received, been intolerant to, been ineligible for or refused
             all treatment known to confer clinical benefit

          -  Meet all requirements for Dose Escalation Phase and Dose Confirmation Phase

        For the Coformulation Phase - Arm K (China only):

          -  Have any histologically- or cytologically-confirmed advanced/metastatic solid tumor by
             pathology report and have received, been intolerant to, been ineligible for, or
             refused all treatment known to confer clinical benefit

          -  Be a Chinese participant residing in China.

        Exclusion Criteria:

          -  For all phases of the study: Has received previous treatment with another agent
             targeting cytotoxic T lymphocyte leukocyte antigen (CTLA)-4

        For Dose Confirmation Phase:

          -  Has received previous treatment with another agent targeting programmed cell death
             protein 1 (PD-1), programmed cell death ligand 1 (PD-L1), or anti PD-L2 agent or with
             an agent directed to another stimulatory or co-inhibitory T-cell receptor

          -  Has had chemotherapy, definitive radiation, or biological cancer therapy within 4
             weeks (2 weeks for palliative radiation) prior to the first dose of study therapy, or
             has not recovered to Common Toxicity Criteria for Adverse Events (CTCAE) Grade 1 or
             better from any AEs that were due to cancer therapeutics administered more than 4
             weeks earlier

          -  Has received lung radiation therapy of >30 Gray (Gy) within 6 months before the first
             dose of study treatment

          -  Is currently participating and receiving study therapy in a study of an
             investigational agent or has participated and received study therapy in a study of an
             investigational agent or has used an investigational device within 28 days of
             administration of quavonlimab.

          -  Has a history of a second malignancy, unless potentially curative treatment has been
             completed with no evidence of malignancy for 3 years

        For Dose Escalation Cohorts (1-3) and Dose Confirmation Arms (A-E):

          -  Has known untreated central nervous system (CNS) metastases. Has known carcinomatous
             meningitis

          -  Has received any prior immunotherapy and was discontinued from that treatment due to a
             Grade 3 or higher immune-related adverse events (irAE)

          -  Has had a severe hypersensitivity reaction to treatment with any monoclonal antibody
             or components of the study drug

          -  Has any active infection requiring therapy

          -  Has a history of interstitial lung disease, history of noninfectious pneumonitis that
             required steroids (or has current pneumonitis), or history of inflammatory bowel
             disease

          -  Has an active autoimmune disease that has required systemic treatment in the past 2
             years

          -  Has clinically significant cardiac disease

          -  Has received a live or live attenuated vaccine within 28 days of planned treatment
             start

          -  Has known history of human immunodeficiency virus (HIV) and/or known active Hepatitis
             B or C infections, and/or known to be positive for hepatitis B surface antigen
             (HBsAg)/ hepatitis B virus (HBV) DNA

          -  Has known psychiatric or substance abuse disorders that would interfere with the
             participant's ability to cooperate with the requirements of the trial

          -  Is pregnant or breastfeeding, or expecting to conceive or father children within the
             projected duration of the study, starting with screening and for up to 120 days
             following cessation of pembrolizumab or pembrolizumab/quavonlimab

          -  Has not fully recovered from any effects of major surgery without significant
             detectable infection

        For Arm F and G (Efficacy Expansion Phase) and Arm J and K (Coformulation Phase) ONLY:

          -  Has known active CNS metastases and/or carcinomatous meningitis

          -  Has not had resolution of anti-PD-1 antibody-related AEs, including immune-mediated
             AEs back to Grade ≤1 or baseline (not applicable to Arm K)

          -  Has not discontinued steroid treatment for an irAE for at least 2 weeks prior to the
             first dose of study drug (not applicable to Arm K)

          -  Has ocular melanoma (not applicable to Arm K)

          -  Has mucosal melanoma (not applicable to Arm K)

          -  Has had an allogenic tissue/solid organ transplant