Efficacy and Safety Study of OMTX705, Monotherapy and Anti-PD-1-combined, in Subjects With Advanced Solid Tumors.

Inclusion Criteria: 1. Male and female patients aged 18 years and older. 2. Part 1 monotherapy and combination: Patients with histologically confirmed advanced (locoregionally recurrent, not amenable to curative therapy) or metastatic solid tumors that have no standard therapeutic option with a proven clinical benefit, or are intolerant to these therapies with any of the following selected tumor histologies: PDAC, gastric cancer (including gastroesophageal junction tumors), head and neck squamous-cell carcinoma (HNSCC), esophageal cancer, NSCLC, high grade serous ovarian cancer, primary peritoneal cancer, mesothelioma, BC, CRC, and FAP positive leiomyosarcoma or other FAP-positive sarcomas (with sponsor's approval). Patients with other tumor histologies may be enrolled with explicit sponsor's approval. Part 2: * SARC1 cohort: patients with locally advanced or metastatic FAP-positive sarcomas that have no standard therapeutic option with a proven clinical benefit or are intolerant to these therapies. FAP-positive is defined as expression of FAP with an H-score ≥40 or 2+/3+ in a tumor biopsy that can be either archival or fresh. FAP positivity will be considered exclusively on sarcoma cells and not in surrounding fibroblasts or other stromal cells. FAP measurement will be done in a central laboratory provided by the sponsor during the screening period (in countries where this is permitted). Alternatively, eligible patients may have had FAP quantified locally before enrolling the trial as part of the previous care of the patient. In the latter case, FAP will be re-quantified retrospectively in a central lab designated by the sponsor. * PDAC\_low and\_high cohorts: patients with metastatic PDAC who have received at least two and no more than four previous lines of systemic treatment for metastatic disease. If the patient received neoadjuvant/adjuvant therapy and recurred \<6 months after the last dose, this line will be counted as the first line for the metastatic disease. * SCHED1 cohort: patients with tumors meeting Part 1 definitions. * BIOPSY cohort: preferentially patients with metastatic CRC, esophageal cancer, GEJ cancer, gastric or NSCLC that have no standard therapeutic option with a proven clinical benefit or are intolerant to these therapies and volunteer for a fresh pre-treatment biopsy during the screening procedure and on-treatment biopsy. Other tumor histologies can be included after approval from the sponsor´s medical monitor. 3. Patients with tumors with actionable mutations should have progress to all approved and locally available targeted therapies or have them contraindicated. 4. Measurable disease by RECIST 1.1 on computerized tomography (CT), positron emission tomography (FDG-PET) or magnetic resonance (MRI) scan. Imaging tests outside the screening period are valid if performed not more than two weeks before consent signature and otherwise fulfil protocol criteria. In sites where available, FAPI-PET can be used but always with an associated CT. 5. Patients should have documented progression to the last line of therapy or, in the opinion of the investigator, require a change in the therapy. This latter option must be discussed and approved explicitly by the sponsor's medical monitor. 6. ECOG performance status 0-1. 7. Serum albumin ≥3.0 g/dL. 8. Adequate bone marrow, hepatic and renal function: 1. Total bilirubin ≤1.5 times upper limit of normal (ULN). 2. Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤3 times ULN, (if liver metastases are present, then ≤5 times ULN is allowed). 3. For Part 1 only: estimated creatinine clearance (CrCL) using the Cockcroft-Gault formula ≥60 mL/minute. Patients with calculated CrCL \<60 mL/min can be enrolled if measured CrCL is ≥60 mL/min. 4. For Part 2 only:, CrCL should be ≥30 mL/min. 5. Hemoglobin ≥9 g/dL (whole or partial blood transfusions not allowed in the two previous weeks before enrollment). 6. Absolute neutrophil count (ANC) ≥1.5 x 109/L (growth factors like G-CSF are not allowed in the two previous weeks before enrollment). 7. Platelet count ≥75 x 109/L (platelet transfusions not allowed in the two previous weeks). 9. Women of childbearing potential (WOCBP) (as defined in Appendix 3) and men with sexual partners who are WOCBP must be willing to adhere to contraceptive requirements as detailed in the protocol (Appendix 3) from at least one month prior to study entry to at least four months after the last dose of study treatment. 10. Suitable venous access for safe drug administration and the study-required drug concentration and PD sampling. 11. For Part 1 only: an archival biopsy for translational research should be available. If the archival biopsy is unavailable or does not have the requirements specified in the sample management plan, it can be replaced with a fresh biopsy. If the archival biopsy is unavailable and the fresh biopsy is not feasible, the medical monitor must approve explicitly the inclusion of the patient. Patients to be enrolled in Part 1 backfilling cohorts should consent for paired screening and on-treatment biopsies. 12. For Part 2 only (Section 6.20.2): i.For patients with sarcoma in the cohort SARC1, an archival or fresh biopsy for FAP quantification during the screening period for eligibility is required. ii.For PDAC\_low, PDAC\_high and BIOPSY cohorts, the patient must consent for fresh paired biopsies. NOTES: (i) In some exceptional circumstances, the medical monitor can waive the obtention of paired treatment biopsies upon request from the investigator. The rationale for the decision needs to be documented in writing. (ii) A patient receiving treatment can decline the on-treatment biopsy without providing any explanation and continue on study. If it is the investigator who decides to skip the on-treatment biopsy the rationale needs to be discussed with the medical monitor and documented in writing. iii.For patients enrolled in the SCHED1 cohort, paired fresh biopsies are desirable but voluntary. Exclusion Criteria: Patients eligible for this study must not meet any of the following criteria: 1. Treatment with systemic anticancer treatments, investigational products, or major surgery within four weeks before the first dose of study drug or five half-lives, whichever is shorter. Subjects should have recovered from previous treatment toxicity to Grade 1, baseline (except alopecia). Patients with endocrinopathies should have the replacement treatment in stable dosing. 2. History of uncontrolled brain metastasis. Subjects with brain metastases are allowed if they are previously treated with surgery, whole-brain radiation, or stereotactic radiosurgery and have new brain imaging confirming that brain metastasis are stable (without evidence of progression by imaging using the identical imaging modality for each assessment, either MRI or CT and considered controlled with \<10 mg/day of prednisone-equivalent at the time of receiving the first dose of OMTX705. For asymptomatic subjects, screening brain imaging is not required. 3. Patient has received extended field radiotherapy ≤four weeks before the start of treatment (≤one week for limited field radiation for palliation), and who has not recovered to Grade 1 or better from related side effects of such therapy (except for alopecia). 4. Active infection requiring parenteral or oral antibiotics. Antibiotics given for prophylaxis are allowed. They are also allowed for minor localized infections like cystitis, tonsilitis or localized skin infections. 5. Evidence of a serious uncontrolled medical disorder that, in the opinion of the investigator or medical monitor, makes it unwise for the subject to participate in the study or that might jeopardize compliance with the protocol. 6. Drainage of ascitic or pleural fluid two or more times in the 4 weeks prior to the first dose of study drug or permanent drain in place (e.g, PleurX®) for ascites or pleural effusion symptom management. 7. Psychiatric illness/social circumstances that would limit compliance with study requirements and substantially increase the risk of AEs or compromised ability to provide written informed consent. 8. Clinical evidence of an active second invasive malignancy with the exception of stable prostate cancer on watchful waiting, in situ cervical cancer, breast ductal carcinoma in situ or localized non-melanoma skin cancers. 9. Uncontrolled or significant cardiovascular disease defined by the New York Hearth Association (NYHA) classification III or IV. 10. History of cerebrovascular stroke or myocardial infarction within the previous three months. 11. Grade ≥2 peripheral neuropathy. 12. Baseline QTc (using the Fridericia correction calculation) \> 470 msec (unless pacemaker in place, only for patients in Part 2) 13. Combination with pembrolizumab/tislelizumab: history of autoimmune disease requiring systemic immunosuppressive therapy (daily prednisone equivalent doses \>10 mg/day). 14. Combination with pembrolizumab/tislelizumab: patients who discontinued prior treatment with any immune checkpoint due to irAEs, irrespective of grade, recovery, or need for continued steroid therapy. Also, subjects without formal contraindication due to previous irAE with any immune checkpoint inhibitor (approved or investigational) are not eligible if the AE has not resolved to Grade 1 or better and/or still requires steroids (\>10 mg of prednisone equivalent per day) for ongoing management. 15. Combination with pembrolizumab/tislelizumab: patients with a history of pneumonitis/interstitial lung disease, patients who received live vaccines within 30 days of enrollment, and patients who discontinued prior immune checkpoint inhibitors due to Grade 2 myocarditis are excluded from enrollment into immune checkpoint inhibitor-containing cohorts. 16. Known hepatitis B virus surface antigen seropositive or detectable hepatitis C infection viral load. Note: Subjects who have positive hepatitis B surface antigen antibody can be included but must have an undetectable hepatitis B viral load. 17. Patients positive for human immunodeficiency virus (HIV) are NOT excluded from this study, but HIV-positive patients must meet the following criteria: 1. have CD4+ T-cell (CD4+) counts ≥350 cells/μL. 2. have not had an opportunistic infection within the past 12 months. Patients on prophylactic antimicrobials can be included in the trial. 3. should be on established antiretroviral therapy for at least four weeks. 4. have an HIV viral load of less than 400 copies/mL prior to enrollment. 5. known history of any other relevant congenital or acquired immunodeficiency other than HIV infection. 18. Known or suspected allergy to study treatment or related products, and specifically patients with a prior history of life-threatening reaction to polysorbate 20. 19. Women who are pregnant or breastfeeding or trying to become pregnant. 20. Male patients wishing fathering children, planning for future sperm banking, or expressing concerns about sterility. 21. Patients requiring the concomitant administration of medications that are strong inhibitors or inducers of CYP3A4, 2D6, 1A2, 2C9, 2B6, and 2C19. In case they are taking any of these drugs (Appendix 4), they should be stopped at least 14 days prior to first dose. 22. For Part 1 only: Only in particular circumstances it will be possible to enroll sarcoma patients with negative FAP expression on the surface of the tumor cells (central lab assessment) or without knowing FAP expression levels before C1D1. However, these cases must be discussed and explicitly approved by the sponsor´s medical monitor.