Inclusion Criteria:  Voluntarily signed and dated written informed consent (IC), obtained prior to any specific study procedure. Age ≥18 years. Eastern Cooperative Oncology Group (ECOG) performance status (PS) ≤1  For the Dose escalation phase:  Patients with pathologically confirmed diagnosis of advanced solid tumors for whom no curative standard therapy exists.  For the Expansion phase:  Patients with pathologically confirmed diagnosis of one of the following malignancies, for whom the standard of care therapies have failed, or are intolerant to standard of care therapies that are known to provide clinical benefit:  Gastrointestinal tumors: colorectal cancer, gastric cancer. Sarcomas: liposarcoma, leiomyosarcoma, synovial sarcoma, Ewing's sarcoma. Tumors with deleterious germline BRCA mutation: epithelial ovarian cancer (including primary peritoneal and fallopian tube cancer), breast cancer, pancreatic cancer, prostate cancer, or any other malignancies. Epithelial ovarian cancer (including primary peritoneal and fallopian tube cancer) with no deleterious germline BRCA mutations or with unknown BRCA status. Adrenocortical carcinoma.  Patients included in the Expansion phase need to meet the following requirements regarding the maximum number of prior chemotherapy regimens (no limit for biological therapies):  Gastrointestinal tumors: no more than three prior chemotherapy lines for colorectal cancer; and no more than two prior chemotherapy lines for gastric cancer. Sarcomas: no more than two prior chemotherapy lines for liposarcoma, leiomyosarcoma and synovial sarcoma; and no more than three prior chemotherapy lines for Ewing's sarcoma. Tumors with deleterious germline BRCA mutation: no more than three prior chemotherapy lines for breast cancer; and no more than two prior chemotherapy lines for prostate cancer, ovarian cancer, pancreatic cancer, gastric carcinoma, or any other malignancies. Epithelial ovarian cancer with unknown BRCA status or no deleterious germline BRCA mutations: no more than three prior chemotherapy lines. Adrenocortical cancer: no more than one prior chemotherapy line (excluding mitotane as single agent or associated with no chemotherapeutic agents).  Note: for the purpose of this criterion, the following situations will be considered as one chemotherapy line:  Adjuvant chemotherapy; neoadjuvant chemotherapy; both adjuvant and neoadjuvant chemotherapy (except if time to relapse was >12 months, in which case it will not be considered as one line); and Change of chemotherapy due to reasons other than PD, such as toxicity (in this case, the two lines will count as a single line). Life expectancy ≥3 months. Patients with measurable or non-measurable disease according to the RECIST v.1.1 are eligible during the dose escalation phase.  Patients included in the Expansion phase must have:  Measurable disease according to the RECIST v.1.1 and/or evaluable disease by serum markers in case of prostate and ovarian cancer (according to the PSAWGR and the GCIG specific criteria, respectively). Confirmed progressive disease after last therapy at study entry. Recovery to grade ≤1 from drug-related AEs of previous treatments, excluding alopecia and grade 1/2 asthenia or fatigue, according to the NCI-CTCAE v.4.  Laboratory values within seven days prior to first infusion:  ANC ≥1.5 x 10^9/L, platelet count ≥100 x 10^9/L and hemoglobin ≥9 g/dL (patients may be transfused for anemia as clinically indicated prior to study entry). AST and ALT ≤3.0 x ULN. Total bilirubin ≤ULN (up to 1.5 x ULN for patients with Gilbert's syndrome). Creatinine clearance ≥30 mL/min (calculated using the Cockcroft and Gault's formula). Serum albumin ≥3 g/dL.  Wash-out periods:  At least three weeks since the last chemotherapy (six weeks if therapy included nitrosoureas or systemic mitomycin C). At least four weeks since the last monoclonal antibody (MAb)-containing therapy or curative radiotherapy (RT). At least two weeks since the last biological/investigational single-agent therapy (excluding MAbs) and/or palliative RT (≤10 fractions or ≤30 Gy total dose). In patients with hormone-sensitive breast cancer progressing while on hormone therapy (except for luteinizing hormone-releasing hormone (LHRH) analogues in pre-menopausal women or megestrol acetate), all other hormonal therapies must be stopped at least one week before study treatment start. Castrate-resistant prostate cancer (CRPC) patients may continue receiving hormone therapy prior to and during study treatment.  Exclusion Criteria:  Concomitant diseases/conditions:  Increased cardiac risk:  Uncontrolled arterial hypertension despite optimal management (≥160/100 mmHg). Presence of clinically relevant valvular disease. History of long QT syndrome. Corrected QT interval (QTcF, Fridericia correction) ≥450 msec on screening electrocardiogram (ECG). History of ischemic heart disease, including myocardial infarction, angina, coronary arteriography or cardiac stress testing with findings consistent with coronary occlusion or infarction ≤6 months prior to study entry. History of heart failure or left ventricular dysfunction (left ventricular ejection fraction [LVEF] below normal values) by multiple-gated acquisition scan (MUGA) or echocardiography (ECHO). ECG abnormalities, including any of the following: left bundle branch block, right bundle branch block with left anterior hemiblock, second (Mobitz II) or third degree atrioventricular block. Symptomatic arrhythmia (excluding anemia-related sinusal tachycardia grade ≤2) or any arrhythmia requiring ongoing treatment, and/or prolonged QT-QTc grade ≥2; or presence of unstable atrial fibrillation. Patients with stable atrial fibrillation on treatment are allowed provided they do not meet any other cardiac or prohibited drug exclusion criterion. Clinically significant resting bradycardia (<50 beats per minute). Concomitant medication with risk of inducing torsades de pointes, which cannot be discontinued or switched to an alternative drug prior to start PM14 dosing. Use of a cardiac pacemaker. Active infection requiring systemic treatment. Known human immunodeficiency virus (HIV) or known hepatitis C virus (HCV) infection or active hepatitis B. Any other major illness that, in the Investigator's judgment, will substantially increase the risk associated with the patient's participation in this study (e.g., COVID-19). Symptomatic, high dose steroid-requiring, and progressing central nervous system (CNS) disease. Exceptions will be made for (i) patients who have completed radiotherapy at least four weeks prior to inclusion (asymptomatic, non-progressing patients taking steroids in the process of already being tapered within two weeks prior to inclusion), and (ii) patients with asymptomatic brain metastasis without need for radiotherapy or steroids. Patients with carcinomatous meningitis regardless of clinical stability. Prior bone marrow or stem cell transplantation, or radiation therapy in more than 35% of bone marrow. Prior treatment with trabectedin or Lurbinectedin (PM01183) within six months prior to onset of study treatment. Use of (strong or moderate) inhibitors or strong inducers of CYP3A4 activity within two weeks prior to the first infusion of PM14. Known hypersensitivity to any of the components of the drug product Limitation of the patient's ability to comply with the treatment or to follow the protocol procedures. Pregnant or lactating women. Women of childbearing potential (WOCBP) must agree to use an effective contraception method to avoid pregnancy during trial treatment and for at least six months after the last infusion. Fertile male patients must agree to refrain from fathering a child or donating sperm and to use an effective contraception method during treatment and for four months after the last infusion. WOCBP who are partners of fertile male patients must use an effective contraception method during the patients' treatment and for four months after the last infusion.