Study of LVGN3616 and LVGN6051±LVGN7409 in Combination With Nab-Paclitaxel or Bevacizumab and Cyclophosphamide in Metastatic Solid Tumors

Inclusion Criteria: To be eligible for this trial, patients must meet all the following eligibility criteria. * Patients must have histologically confirmed metastatic solid tumors with pre-identified molecular profiling in a Clinical Laboratory Improvement Amendments (CLIA)-certified laboratory, either refractory to standard therapy or for which no effective standard therapy that increases survival for at least 3 months is available, or they declined standard of care therapy (the treating physician needs document reasons for a patient to decline standard of care therapy and provide justification for participating this study in the medical record, which will be recorded in eCRF). * Measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1. * Male or female aged ≥18 years. * Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1. * Adequate organ functions as defined below: * Absolute neutrophil count (ANC) ≥ 1,500 /μL. * Hemoglobin (Hb) ≥ 8.5 g/dL. * Platelets ≥ 100,000 /μL for nab-paclitaxel or ≥ 75,000 /μL for cyclophosphamide. * Total bilirubin ≤ 1.5 × upper limit of normal (ULN); or total bilirubin \< 3.0 × ULN with direct bilirubin ≤ ULN in patients with well documented Gilbert's Syndrome. * ALT and AST ≤ 2.5 × ULN. * Serum albumin ≥ 3 g/dL. * Urinalysis ≤ 1 proteinuria, or urine protein/creatinine ratio (UPCR) ≤ 1 mg/mg (≤ 113.2 mg/mmol), or 24-h urine protein ≤ 1 g (apply to bevacizumab-based regimens only). * PT/INR or partial thromboplastin time (PTT) test \< 1.3 × the laboratory ULN if not on therapeutic anticoagulation. * Serum creatinine ≤ 1.5 × ULN or calculated creatinine clearance (CrCl) ≥ 45 mL/min by the Cockcroft-Gault method\* or 24-hour urine collection. * CrCl = (140-age) x (weight/kg) x Fa / (72 x serum creatinine mg/dL). \^a where F= 0.85 for females and F=1 for males * Women of child-bearing potential (WOCBP) must have a negative serum pregnancy test within 3 days prior to initiation of therapy (C1D1) and must agree to use effective birth control during the study prior to the first dose and for at least 6 months after the last dose. Female patients are not considered to be of child-bearing potential if they are post-menopausal (no menses for 12 months without an alternative medical cause) or permanently sterile (hysterectomy, bilateral salpingectomy, or bilateral oophorectomy). Male patients must agree to abstain or use barrier contraception (i.e., condoms) and avoid sperm donation for the duration of the study and for 6 months after treatment stops. * Ability to read and fully understand the requirements of the trial, willingness to comply with all trial visits and assessments, and willingness and ability to sign an institutional review board (IRB)-approved written informed consent document (ICD). Patients with Impaired Decision-Making Capacity (IDMC) must have a close caregiver or Legally Authorized Representative (LAR). For remote and In-person consenting, we will follow the Office of Clinical Research SOP:04 Informed Consent Process. * Any prior palliative radiation must have been completed at least 7 days prior to the start of study drugs, and patients must have recovered from any acute adverse effects prior to the start of study treatment (Radiotherapy for extended field within 2 weeks or limited field radiotherapy within 1 week). * Fridericia's corrected QT interval (QTcF =QT/∛(60/HR) ) ≤ 460 milliseconds (ms) for males and ≤ 480 ms for females on ECG conducted at rest during Screening. Note: Patients with an atrioventricular pacemaker or other condition (for example, right bundle branch block) that renders the QT measurement invalid are an exception and this criterion does not apply. * Agreeing to provide an archival tissue block, or 10 formalin-fixed paraffin-embedded (FFPE) slides if available. * Prior treatment with immunotherapy, taxane, VEGF inhibition or cyclophosphamide is allowed. However, prior immunotherapy with anti-PD1/PD-L1 plus a CD137 agonist or a CD40 agonist is not allowed. Exclusion Criteria: Patients who meet any of the following criteria will be not eligible for the study: * Any treatment specifically for systemic tumor control given within 3 weeks before the initiation of therapy; within 2 weeks if cytotoxic agents were given weekly, within 6 weeks for nitrosoureas or mitomycin C; within 5 half-lives for targeted agents with half-lives and pharmacodynamic effects lasting \< 5 days; or failure to recover from toxic effects of any previous therapy. A drug that has not received regulatory approval for any indication within 14 or 21 days of treatment for a non-myelosuppressive or myelosuppressive agent, respectively: patients must recover for previous cancer therapy, and are ready to proceed with further cancer therapy. * Uncontrolled intercurrent illness including but not limited to: * ongoing or active infection requiring intravenous antibiotics * symptomatic congestive heart failure (New York Heart Association Class III or IV) * history of myocardial infarction, unstable angina, stroke or transient ischemic attack within 6 months before study enrollment * lesions invading or encasing any major blood vessels and cavitating pulmonary lesion(s) or known endotracheal or endobronchial disease manifestation. Uncontrolled hypertension defined as sustained blood pressure (BP) \> 140 mm Hg systolic or \> 90 mm Hg diastolic despite optimal antihypertensive treatment (apply to bevacizumab-based regimens only) * history or current evidence of uncontrolled ventricular arrhythmia * congenital long QT syndrome, or any known history of torsade de pointes, or family history of unexplained sudden death * clinically significant bleeding or active gastric or duodenal ulcer * chronic diarrhea diseases considered to be clinically significant by investigator * Abdominal fistula, GI perforation, bowel obstruction, or intra-abdominal abscess within 6 months before first dose of study treatment, or any gastrointestinal disorders associated with a high risk of perforation or fistula formation * other severe acute or chronic medical or psychiatric condition or laboratory abnormality that may increase the risk associated with study participation, or may interfere with the interpretation of study results, and in the judgment of the Investigator would make the patient inappropriate for entry into this study Note: Subjects with a diagnosis of incidental, subsegmental pulmonary embolism or deep vein thrombosis are allowed if stable, asymptomatic, and treated with a stable dose of permitted anticoagulation for at least 1 week before first dose of study treatment. * Unresolved clinically significant Grade 1 or higher toxicity from prior therapy. * History of allergic reactions to the study drugs, or any component of the products. * Presence of other active invasive cancers that requires active treatment other than hormonal therapy. * Having not recovered from a major surgical procedure or significant traumatic injury (i.e., still needing additional surgical or medical care for these issues): major surgical procedures ≤ 28 days of treatment entry, or minor surgical procedures ≤ 7 days. No waiting period required following port-a-cath or other central venous access placement. Subjects must have complete wound healing from major surgery or minor surgery before first dose of study treatment. Subjects with clinically relevant ongoing complications from prior surgery are not eligible. * Currently receiving an investigational drug in a clinical trial or participating in any other type of medical research judged not to be scientifically or medically compatible with this study. If a patient is currently enrolled in a clinical trial involving non-approved use of a therapeutic device for cancer control, then agreement with the investigator and the sponsor (MD Anderson IND Office) is required to establish eligibility. * Has received a live vaccine within 30 days prior to the first dose of study drug. Examples of live vaccines include, but are not limited to, the following: Bacille Calmette-Guérin vaccine, measles, mumps, rabies, rubella, typhoid vaccine, varicella/zoster, and yellow fever. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines are live attenuated vaccines and are not allowed. COVID19 vaccines including killed virus are allowed. * Caution should be exercised when administering nab-paclitaxel concomitantly with known substrates or inhibitors of CYP2C8 and CYP3A4 (https://www.fda.gov/drugs/drug-interactions-labeling/drug-development-and-drug-interactions-table-substrates-inhibitors-and-inducers). * Symptomatic primary tumors or metastasis in the brain and/or central nervous system that are uncontrolled with antiepileptics and/or require steroids at a dose of prednisone \> 10 mg/day or equivalent. * Evidence of leptomeningeal or lymphangitic carcinomatosis. * A history of another primary malignancy that is currently clinically significant, requiring active intervention except for hormone therapy. * Lactation or pregnancy. * Human immunodeficiency virus requiring HAART treatment due to unknown drug-drug interactions or has known active hepatitis B (e.g., HBsAg reactive) or C virus (e.g., HCV RNA \[quantitative\] is detected) infection: patients who have had active HBV or HCV infections in the past but have evidence of viral clearance as shown by negative viral load, i.e., undetectable HBV DNA or HCV RNA, will be eligible. * Concurrent immunosuppressive therapy or steroid (\> 10 mg/day prednisone or equivalent). * History of autoimmune disease including but not limited to inflammatory bowel disease, myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, Wegener's granulomatosis, Sjögren's syndrome, Guillain-Barré syndrome, multiple sclerosis, vasculitis, or glomerulonephritis, which requires systemic therapy in the past 2 years. * Note: Patients with vitiligo, resolved childhood asthma/atopy, hypothyroidism on stable hormone replacement, controlled asthma, Type I diabetes, Graves' disease, or Hashimoto's disease, are not excluded. * History of grade ≥ 3 immune-related adverse events with previous immunotherapy. Note: Patients with adequately treated skin rash other than Steven-Johnson, toxic epidermal necrolysis of other severe forms of dermatitis; or replacement therapy for endocrinopathies, are not excluded. * History of interstitial lung disease or (non-infectious) pneumonitis that required steroids or current pneumonitis. * History of grade ≥ 3 allergic reaction to treatment with a monoclonal antibody. * Patients with Urinary Outflow Obstruction (apply to cyclophosphamide-based regimens only).