Inclusion Criteria:

1. Able and willing to participate and comply with all study requirements and provide signed and dated informed consent prior to initiation of any study procedures;
2. Histologically or cytologically confirmed advanced/metastatic extracranial solid tumor malignancy:

1. Stages 1 and 2: Subjects must have received, have been intolerant to, have been ineligible for, or have declined all treatment known to confer clinical benefit with the exception of subjects enrolled in combination cohorts with a PD-1i, where a PD-1i is approved by the local regulatory agencies;
2. Stage 3: This stage may enroll subjects with 3L/4L PD-(L)1-naïve, platinum-resistant ovarian cancer;
3. Stage 4: This stage may enroll subjects with the following cancers:

1. 2L/3L ccRCC. Subjects must have progressed on or after treatment with an anti-PD-(L)1 agent in their most recent prior line of therapy;
2. 2L-4L TNBC. Subjects must have progressed on or after treatment with a prior anti-PD-(L)1 therapy;
3. 1L, PD-(L)1-naïve, PD-L1+; combined positive score (CPS) ≥1% HNSCC;
4. 2L/3L platinum-experienced HNSCC. Subjects must have progressed on or after treatment with an anti-PD-(L)1-agent in their most recent prior line of therapy;
5. 3L/4L, PD-(L)1-naïve, platinum-resistant ovarian cancer;
6. 2L/3L NSCLC. Subjects must have progressed on or after treatment with platinum-based chemotherapy and an anti-PD-(L)1-containing therapy. The anti-PD-(L)1 agent must have been a part of the most recent prior line of therapy. Subjects with EGFR mutations and ALK rearrangements will be excluded. Subjects with other targetable genomic aberrations for which FDA approved therapies exist must have received appropriate FDA-approved targeted therapy;
7. 2L/3L cSCC. Subjects must have progressed on or after treatment with an anti-PD-(L)1 agent in their most recent prior line of therapy;
8. 2L-4L PD-(L)1-naïve undifferentiated pleomorphic sarcoma (UPS) and liposarcoma (LPS);
9. 2L/3L biliary tract cancer (BTC), including intra- and extra-hepatic biliary duct cancer and cancer of the gallbladder. Subjects must have progressed on or after gemcitabine/cisplatin (Gem/Cis) in the metastatic setting and must have PD-(L)1 inhibitor resistance. Subjects with FGFR and IDH1 mutations must have progressed on or after targeted therapies for these mutations;
10. Measurable disease, according to the RECIST version 1.1, that has objectively progressed since (or on) previous treatment as assessed by the Investigator;
11. ≥18 years of age;
12. Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1;
13. Predicted life expectancy of ≥3 months;
14. Have specified laboratory values (obtained ≤28 days prior to planned Cycle 1, Day 1 [C1D1]) in accordance with the study protocol;
15. For women of childbearing potential (WOCBP): negative serum pregnancy test during the Screening period and a negative urine pregnancy test up to 24 hours in advance of C1D1;
16. WOCBP and males whose partners are WOCBP must agree to use a highly effective method of birth control throughout their participation and for 5 months following the last study drug administration.

Exclusion Criteria:

1. Concurrent anticancer treatment, either FDA approved or investigational, for the cancer being evaluated in this study or for prior malignancies. A past history of other malignancies is allowed as long as the subject is not receiving treatment other than hormonal therapy and, in the judgment of the Investigator, is unlikely to have a recurrence. Of note, concurrent malignancies that do not require treatment and are clinically stable are allowed;
2. Prior infusion of JTX-8064, LILRB2, or ILT4-directed therapy;
3. The therapies listed below within the specified timeframe or ongoing toxicity attributed to prior therapy that was >Grade 1 according to the NCI CTCAE, version 5.0. Exceptions: >Grade 1 toxicities that, in the opinion of the Investigator, should not exclude the subject (e.g., alopecia, Grade 2 neuropathy, hypo- or hyperthyroidism, or other endocrinopathies that are well controlled with hormone replacement) and are approved by the Medical Monitor:

1. Major surgery (excluding minor procedures, for example, placement of vascular access, gastrointestinal/biliary stent, biopsy) <4 weeks prior to planned C1D1;
2. Immunotherapy or biologic therapy <28 days prior to planned C1D1 or 5 half-lives, whichever is shorter;
3. Chemotherapy <21 days prior to planned C1D1, or <42 days for mitomycin or nitrosoureas or 5 half-lives, whichever is shorter;
4. Targeted small molecule therapy <14 days or 5 half-lives, whichever is shorter, prior to planned C1D1;
5. Hormonal or other adjunctive therapy for cancers other than the cancer under evaluation in this study that started <14 days prior to planned C1D1 are not permitted; however, antiestrogen therapy, bisphosphonates, somatostatin analogues, leuprolide, and denosumab are permitted if started ≥14 days prior to C1D1. Other hormonal treatments and/or treatment for stable cancers (other than the cancer being treated on-study) may also be permitted 1) if these therapies would not be expected to have any positive or negative effect on the cancer being treated and 2) if discussed with and approved by the Medical Monitor;
6. Radiation therapy <21 days prior to planned C1D1. Exception: Limited (e.g., pain palliation) radiation therapy is allowed prior to and during study drug administration as long as there are no acute toxicities, any AE due to prior radiation therapy has recovered to
7. Any prior organ transplantation, including allogeneic or autologous stem cell transplantation;
8. History of intolerance, hypersensitivity, or treatment discontinuation due to Grade 3 or greater irAEs (related to prior immunotherapy);
9. Diagnosis of immunodeficiency, either primary or acquired, or treatment with immunosuppressive levels of systemic corticosteroids (equivalent to ≥10 mg prednisone per day) or any other form of immunosuppressive therapy within 7 days prior to planned C1D1. Exception: Inhaled, intra-articular, topical, or systemic corticosteroids (systemic only at doses intended for adrenal replacement) and doses of immunosuppressive agents used prophylactically for contrast allergies are permitted in the absence of active autoimmune disease;
10. Known severe intolerance or life-threatening hypersensitivity reactions to humanized mAbs or IV immunoglobulin preparations; any history of anaphylaxis; known allergy to any of the study medications, their analogues, or excipients (sodium acetate, sucrose, sodium chloride and polysorbate 80) in the various formulations of any agent;
11. Symptomatic or uncontrolled brain metastases, leptomeningeal disease, or spinal cord compression not definitively treated with surgery or radiation (brain metastases that are stable and asymptomatic after prior treatment will be allowed);
12. Active and clinically relevant bacterial, fungal, or viral infection, including known hepatitis A, B, or C, or HIV (testing not required);
13. Women who are pregnant or breastfeeding or who plan to become pregnant/breastfeed while on study; men who plan to father children during the study;
14. History of pneumonitis requiring treatment with corticosteroids, interstitial lung disease, or severe (≥Grade 3) radiation pneumonitis (excluding localized radiation pneumonitis);
15. History in the last 3 months of acute diverticulitis, intra-abdominal abscess, or gastrointestinal obstruction, unless approved by Medical Monitor;
16. Symptomatic cardiac or cerebrovascular disease that is unresponsive to surgical or medical management;
17. Medical or social condition that, in the opinion of the Investigator, might place the subject at increased risk, adversely affect compliance, or confound safety or other clinical study data interpretation;
18. Active disease requiring systemic immunosuppressive therapy;
19. Live vaccines ≤30 days of C1D1;
20. Deep vein thrombosis, pulmonary embolism (including asymptomatic pulmonary embolism identified on imaging), or other thromboembolic event within the 6 months preceding C1D1 for JTX-8064 monotherapy cohorts only.