XmAb23104 (PD1 X ICOS) and XmAb22841 (CTLA-4 X LAG3) in Treating Melanoma Prior Immune Checkpoint Inhibitor Therapy

Inclusion Criteria: 1. Participants must have a histologically or cytologically confirmed advanced/metastatic melanoma by pathology report. Participants with cutaneous, mucosal, acral and unknown primaries will be allowed. 2. Participants must have progressed on either single agent programmed cell death protein 1 (PD1) or combination PD1/ cytotoxic T-lymphocyte-associated protein 4 (CTLA-4) inhibition therapy. 3. Participants are allowed to have up to 4 prior lines of therapy in the metastatic setting. NOTE: Prior BRAF targeted therapies are allowed. Prior exposure to immunotherapeutics is allowed, including LAG-3, PD1, and PD-L1 inhibitors, provided participant did not experience a \>= Grade 3 (CTCAE v5.0) drug-related toxicity on monotherapy with a Expression of lymphocyte activation gene 3 (LAG-3), PD1, or programmed death-ligand 1 (PD-L1) inhibitor. 4. For Dose Escalation Phase, central nervous system (CNS) disease is not required, but it is permitted, provided the following three CNS criteria are met: A. CNS lesions must be asymptomatic and stable, as determined by stability on magnetic resonance imaging (MRI) at least 4 weeks prior to study enrollment. B. Prior radiation treatment to CNS lesions will be allowed; however, the participant must have recovered from prior toxicities as described in Exclusion #2. C. Brain lesions \>= 5 mm are allowed. NOTE: See also exclusion criterion #5 for additional CNS requirements. 5. For Dose Expansion Phase: * Participants in Expansion Arm A must have metastatic melanoma without CNS disease * Participants in Expansion Arm B must have metastatic melanoma with CNS disease, and the following three CNS criteria must be met: A. CNS lesions must be asymptomatic and stable, as determined by stability on MRI at least 4 weeks prior to study enrollment. B. Prior radiation treatment to CNS lesions will be allowed; however, the participant must have recovered from prior toxicities as described in exclusion criteria #2. C. Brain lesions \>= 5 mm are allowed. NOTE: See also exclusion criterion #5 for additional CNS requirements. 6. Participants must have measurable disease according to RECIST 1.1 with the following modification for brain lesions (if brain lesions are present): \- Measurable brain lesions are defined as those that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 5 mm. Measurable lesions for all other non-brain sites are defined as those that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>=20 mm (\>=2 cm) by chest x-ray or as \>=10 mm (\>=1 cm) with Computerized tomography (CT) scan, MRI, or calipers by clinical exam. NOTE: MRI brain (or equivalent brain imaging) is required at baseline for all patients to characterize brain disease status. 7. Age \>=18 years. 8. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 (Karnofsky \>60%). 9. Demonstrate adequate organ function as defined below obtained within 14 days prior to the start of study treatment: NOTE: Criteria must be met without packed red blood cell (pRBC) and platelet transfusion within the prior 2 weeks. Participants can be on a stable dose of erythropoietin (\>=approximately 3 months). Bone Marrow: a) Absolute neutrophil count \>=1,500/microliter (mcL) b) Platelets \>=100,000/mcL c) Hemoglobin \>=9 g/dL or \>5.6 mmol/L Renal: d) Serum creatinine or creatinine clearance (CrCl) (measured or calculated per institutional standard) OR for participants with creatinine levels \>1.5 × upper limit of normal (ULN): Glomerular Filtration Rate (GFR) must be assessed, Creatinine \<=1.5 × ULN OR for participants with creatinine levels \>1.5 × ULN: GFR \>30 mL/min/1.73 m\^2 calculated per institutional standard method. Hepatic: e) Total bilirubin (serum) \<=1.5 × ULN, unless elevated due to Gilbert's syndrome and direct bilirubin is within normal limits. f) Aspartate aminotransferase (AST)/ (serum glutamic-oxaloacetic transaminase (SGOT) ) \<=2.5 x ULN or For participants with liver metastasis: \<=5 x ULN g) Alanine aminotransferase (ALT)/(serum glutamic-pyruvic transaminase (SGPT)) \<=2.5 x ULN or For participants with liver metastasis: \<= 5 x ULN Coagulation: h) International Normalized Ratio (INR) or Prothrombin Time (PT) or Activated Partial Thromboplastin Time (aPTT) \<1.5 ULN (unless participant is on therapeutic anticoagulant therapy, in which case the PT/INR or aPTT should be within the range of intended use for the anticoagulant(s)). 10. For HIV-infected participants, participants must have well controlled HIV on anti-retroviral therapy (ART), defined as: a) Participants on ART must have a CD4+ T-cell count \>350 cells/mm3 at time of screening. b) Participants on ART must have achieved and maintained virologic suppression defined as confirmed HIV RNA level below 50 or the lower limit of quantitation (LLOQ) (below the limit of detection) using the locally available assay at the time of screening and for at least 12 weeks prior to screening. c) Participants on ART must have been on a stable regimen, without changes in drugs or dose modification, for at least 4 weeks prior to initiating the study intervention. d) The combination ART regimen must not contain any antiretroviral medications other than: abacavir, dolutegravir, emtricitabine, lamivudine, raltegravir, rilpivirine, or tenofovir. 11. The effects of XmAb23104 and XmAb22841 on the developing human fetus and nursing infant are unknown. Additionally, it is not known if XmAb23104 and XmAb22841 have transient adverse effects on the composition of sperm. Therefore, participants who enroll in this trial must agree to follow the below contraception requirements. Contraception Requirements for Females: * Female participants should immediately inform the investigator if they become pregnant or suspect pregnancy while participating in the trial. * Female participants of reproductive potential must agree to remain abstinent or use a highly effective method of contraception £ while receiving trial therapy and for 150 days following completion of trial therapy. Women also must not freeze or donate eggs during this same period. Contraception Requirements for Males: * Male participants should immediately inform the investigator if their partner becomes pregnant or suspects pregnancy while they are participating in the trial. * With a female partner of reproductive potential, males must agree to remain abstinent or use a highly effective method of contraception £ while receiving trial therapy and for 150 days following completion of trial therapy. Men also must not donate sperm during this same period. * With a pregnant female partner, males must remain abstinent or use a condom while receiving trial therapy and for 150 days following completion of trial therapy to avoid exposing the embryo/child. * With a lactating female partner, males must remain abstinent or use a condom while receiving trial therapy and for 150 days following completion of trial therapy to avoid exposing the nursing infant. NOTE: A woman is considered NOT to be of reproductive potential (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice), if she meets either of the following two criteria: 1. has reached a postmenopausal state (\>= 12 continuous months of amenorrhea with no identified cause other than menopause) 2. has undergone surgical sterilization (i.e., hysterectomy and/or bilateral oophorectomy for removal of uterus and/or ovaries) NOTE: Sexual abstinence is defined as not engaging in heterosexual intercourse. Sexual abstinence is permitted only if it is the preferred and usual lifestyle of the individual. Periodic abstinence (e.g., calendar, ovulation, symptothermal, postovulation methods) and withdrawal are not adequate methods of contraception. NOTE: Highly effective methods of birth control include hormonal birth control that is initiated at least 14 days prior to the first dose of trial therapy \[oral, intravaginal, transdermal, implantable, or intrauterine devices (IUDs)\], IUDs (non-hormonal), male vasectomy, or any double-barrier method (combination of male condom and spermicide with either cap, diaphragm, or sponge). 12\. Females of reproductive potential (defined in inclusion criterion #11) must have a negative urine or serum pregnancy test (i.e., human chorionic gonadotropin test) within 72 hours before the first dose of study intervention. NOTE: If a urine pregnancy test cannot be confirmed as negative (e.g., an ambiguous result), a serum pregnancy test is required. In such cases, the participant must be excluded from participation if the serum pregnancy result is positive. 13\. Individuals with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. 14\. Participant (or the participant's legally authorized representative if the participant has impaired decision-making capacity) must have the ability to understand and the willingness to sign a written informed consent document. NOTE: The participant/Legally Authorized Representative (LAR) may elect to provide consent for optional participation in future biomedical research (FBR). However, the participant may participate in the main study without participating in the optional FBR. Exclusion Criteria: 1. Is currently receiving any of the following therapies and unable or unwilling to discontinue their use prior to starting study drugs: 1. chemotherapy, definitive radiation, or biological cancer therapy 2. palliative radiation 3. investigational agent(s) 4. investigational device(s) NOTE: Prior exposure to immunotherapeutics is allowed, including PD-1 and PD-L1 inhibitors, provided participant did not experience a \>= Grade 3 drug-related toxicity on monotherapy with a PD-1 or PD-L1 inhibitor. NOTE: Radiation therapy to a symptomatic solitary lesion or to the brain may be allowed at the investigator's discretion after the DLT observation period. 2. Has not recovered from any adverse events (AE) that are due to receipt of prior cancer therapeutics (such as chemotherapy, definitive radiation, biological cancer therapy, palliative radiation), investigational agent(s), or investigational device(s). (This includes participants with previous immunomodulatory therapy with residual immune-related AEs). Event recovery is defined as improvement to CTCAE (v5.0) Grade 1 or baseline, possible exceptions include: 1. Any grade alopecia and endocrinopathies that, in the judgement of the investigator, can be clinically managed. 2. Clinically managed \<= Grade 2 itching associated with past treatment. 3. Has had more than 4 lines of prior therapy in the metastatic setting. NOTE: Prior exposure to immunotherapeutics is allowed, including PD-1 and PD-L1 inhibitors, provided participant did not experience a \>= Grade 3 drug-related toxicity on monotherapy with a PD-1 or PD-L1 inhibitor. 4. Has any history of Grade 3 or 4 (CTCAE v.5.0) immune-related adverse events, that are unresolved, with the exceptions of endocrinopathies that can be clinically managed in the judgement of the investigator. 5. Has clinically active central nervous system (CNS) metastases and/or carcinomatous meningitis or stable CNS lesions requiring ongoing steroid treatment of greater than 10 mg/day of prednisone or alternative dose-equivalent 6. Has had a severe hypersensitivity reaction to treatment with the monoclonal antibody/components of the study intervention (XmAb22841 or XmAb23104 or their excipients). 7. Has a diagnosis of immunodeficiency. 8. Has an active infection requiring therapy that is not stable or controlled in the judgement of the investigator. 9. Has a prior history of \>= Grade 2 (CTCAE v5.0) pneumonitis or current pneumonitis of any Grade. 10. Has an active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease-modifying agents, corticosteroids, or immunosuppressive drugs), except vitiligo or resolved childhood asthma/atopy. NOTE: Replacement therapy, such as thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, is not considered a form of systemic treatment and is allowed. 11. Is on chronic systemic steroid therapy in excess of replacement doses (prednisone \<=10 mg/day is acceptable), or on any other form of immunosuppressive medication. Use of nonsystemic steroids is permitted. 12. Participants with known Hepatitis B or C infections or known to be positive for Hepatitis B antigen (HBsAg)/Hepatitis B virus (HBV) DNA or Hepatitis C Virus (HCV) Antibody or RNA and who are not stable on treatment. Active Hepatitis C is defined by a known positive Hep C Ab result and known quantitative HCV RNA results greater than the lower limits of detection of the assay. 13. HIV-infected participants with a history of Kaposi's sarcoma and/or Multicentric Castleman's Disease. 14. Has undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years; or has undergone transplant greater than 5 years ago and has any symptoms of graft versus-host disease. 15. Is pregnant or intending to conceive or father children within the projected duration of the study, starting with the screening visit through 120 days after the last dose of study intervention. NOTE: These participants are excluded because there is an unknown but potential risk for adverse events to the developing fetus. 16. Is breastfeeding or intending to breastfeed from the time of the first dose of study therapy through 120 days after the last dose of the study intervention. NOTE: It is unknown whether XmAb23104 \& XmAb22841 are excreted in human milk. Breastfeeding participants are excluded due to the potential for serious adverse reactions in the nursing infant. 17. Has not fully recovered from any effects of major surgery or currently has significant detectable post-surgical infection. 18. Has received a live vaccine within 30 days prior to the first dose of trial therapy. NOTE: Examples of live vaccines include, but are not limited to the following: measles, mumps, rubella, varicella/zoster, yellow fever, rabies, Bacillus Calmette-Guerin, and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., Flu Mist®) are live-attenuated vaccines and are not allowed. Coronavirus disease of 2019 (COVID-19) vaccines are generally killed virus vaccines and are allowed. 19. Has a known psychiatric or substance abuse disorder that would interfere with the participant's ability to cooperate with the requirements of the study. 20. Has a history or evidence of any other clinically unstable/uncontrolled disorder, condition, or disease other than their primary malignancy, that in the opinion of the Investigator would pose a risk to patient safety or interfere with study compliance, evaluations, procedures, or completion.