MTI-301 for the Treatment of Metastatic or Unresectable and Refractory Solid Cancers

Inclusion Criteria: * Age ≥ 18 years. * Histologically or cytologically confirmed solid tumor (cancer) that is metastatic or unresectable and who are refractory to or intolerant of existing, standard-of-care therapy(ies), known to provide clinical benefit for their condition. * Measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) criteria or evaluable disease. * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2. * Hemoglobin ≥ 9.0 g/dL (obtained ≤ 28 days prior to registration). * Absolute neutrophil count (ANC) ≥ 1500/mm\^3 (obtained ≤ 28 days prior to registration). * Platelet count ≥ 100,000/mm\^3 (obtained ≤ 28 days prior to registration). * Total bilirubin ≤ 1.5 x upper limit normal (ULN). Patients with Gilbert's syndrome: Total bilirubin ≤ 3 x ULN (obtained ≤ 28 days prior to registration). * Alanine aminotransferase (ALT) and aspartate transaminase (AST) ≤ 3 x ULN (≤ 5 x ULN for patients with liver involvement) (obtained ≤ 28 days prior to registration). * Prothrombin time (PT)/international normalized ratio (INR)/activated partial thromboplastin time (aPTT) =\< 1.5 x ULN OR if patient is receiving anticoagulant therapy and INR or aPTT is within target range of therapy as determined by treating investigator (obtained ≤ 28 days prior to registration). * Calculated creatinine clearance ≥ 60 mL/min using the Cockcroft-Gault formula (obtained ≤ 28 days prior to registration). * Negative pregnancy test done ≤ 7 days prior to registration, for persons of childbearing potential only. * NOTE: If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * Provide written informed consent. * Ability to complete questionnaire(s) by themselves or with assistance. * Willingness to provide mandatory blood specimens for correlative research. * Willingness to provide mandatory tissue specimens for correlative research. * Willing to return to enrolling institution for follow-up (during the Active Monitoring Phase of the study). Exclusion Criteria: * Any of the following because this study involves an investigational agent whose genotoxic, mutagenic, and teratogenic effects on the developing fetus and newborn are unknown: * Pregnant persons * Nursing persons * Persons who are of childbearing potential who are unwilling to employ adequate contraception. * NOTE: For the purpose of this guidance, methods that can achieve a failure rate of less than 1% per year when used consistently and correctly are considered as highly effective birth control methods. Such methods include: * Combined (estrogen and progestogen containing) hormonal contraception associated with inhibition of ovulation \[Hormonal contraception may be susceptible to interaction with the investigational medicinal product (IMP), which may reduce the efficacy of the contraception method.\]: * Oral * Intravaginal * Transdermal * Progestogen-only hormonal contraception associated with inhibition of ovulation (Hormonal contraception may be susceptible to interaction with the IMP, which may reduce the efficacy of the contraception method.): * Oral * Injectable * Implantable (Contraception methods that in the context of this guidance are considered to have low user dependency.) * Intrauterine device (IUD) (Contraception methods that in the context of this guidance are considered to have low user dependency) * Intrauterine hormone-releasing system (IUS) (Contraception methods that in the context of this guidance are considered to have low user dependency.) * Bilateral tubal occlusion (Contraception methods that in the context of this guidance are considered to have low user dependency.) * Vasectomised partner \[Contraception methods that in the context of this guidance are considered to have low user dependency. Vasectomised partner is a highly effective birth control method provided that partner is the sole sexual partner of the women of childbearing potential (WOCBP) trial participant and that the vasectomised partner has received medical assessment of the surgical success.\] * Sexual abstinence (In the context of this guidance sexual abstinence is considered a highly effective method only if defined as refraining from heterosexual intercourse during the entire period of risk associated with the study treatments. The reliability of sexual abstinence needs to be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the subject.). * Any of the following prior therapies: * Major surgery ≤ 3 weeks prior to registration * Chemotherapy ≤ 2 weeks prior to registration * Immunotherapy ≤ 3 weeks prior to registration * Radiation ≤ 2 weeks prior to registration. * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens. * Immunocompromised patients and patients known to be HIV positive and currently receiving antiretroviral therapy, patients with hepatitis B and C on active treatment, or those with acute hepatitis B and C not currently on treatment. * NOTE: Patients known to be HIV positive, but without clinical evidence of an immunocompromised state, are eligible for this trial. * Uncontrolled intercurrent illness including, but not limited to: * Ongoing or active infection * Symptomatic congestive heart failure * Unstable angina pectoris * Clinically significant cardiac arrhythmia * Bleeding disorder * Cardiac arrhythmia * Psychiatric illness/social situations that would limit compliance with study requirements * Dyspnea at rest due to complications of advanced malignancy or other disease that requires continuous oxygen therapy * Any other conditions that would limit compliance with study requirements. * History of myocardial infarction ≤ 6 months prior to registration, or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias. * Other active malignancy ≤ 3 years prior to registration. * EXCEPTIONS: Non-melanotic skin cancer or carcinoma-in-situ of the cervix. * NOTE: If there is a history of prior malignancy, they must not be receiving other specific treatment for their cancer. * Unresolved toxicity from prior chemotherapy (subjects must be recovery to ≤ grade 1 toxicity from previous anticancer treatments or previous investigational agents). * Receiving any other investigational agent or device ≤ 14 days prior to registration. * Planning on receiving other medical, surgical, or radiological cancer treatments during the course of this study. * Evidence of untreated fluid retention at the time of registration (including, for example, peripheral edema, pleural effusion, or ascites on physical or radiological examination) or history of severe capillary leak syndrome. * Any other condition which the investigator believes would make participation in the study not acceptable. * Subjects with any active and/or symptomatic brain metastases or active primary central nervous system (CNS) and subjects with carcinomatosis meningitis are excluded. * NOTE: History of brain metastases treated by surgery and/or radiotherapy provided neurologically stable and off steroids ≥ 4 weeks prior to registration are allowed. * Grade 2 or greater neuropathy (excluding diagnosed carpal tunnel syndrome). * Use of concomitant medication that are known to be inhibitors or substrates of major CYP enzymes, CYP2C9, CYP2c19, CYP3a4, CYP2D6, CYP1A2, CYP2B6 and CYP2C8 ≤ 14 days prior to registration. * Use of concomitant medication that are known to be inhibitors or substrates of transporters ≤ 14 days prior to registration. * Corrected QT (QTc) prolongation based on QTc interval prior to registration of ≥ 470 ms using the Fridericia's formula (QTcF). * Confluent superficial keratitis, a cornea epithelial defect, a corneal ulcer or stromal opacity. * Significant electrolyte imbalance. * Significant uncontrolled congestive heart failure. * Symptomatic uncontrolled cardiac arrhythmia. * Genetic predisposition for long QT syndrome. * Subjects who are receiving concomitant QT prolonging medication.