ALRN-6924 and Paclitaxel in Treating Patients With Advanced, Metastatic, or Unresectable Solid Tumors

Inclusion Criteria: In order to be eligible to participate in this study, an individual must meet all of the following criteria: 1. 18 years of age or older 2. Histologically- or cytologically-confirmed solid tumors (excluding lymphomas) that are metastatic or unresectable and that meet the following criteria: 1. Escalation and expansion cohorts: wild type (WT) TP53 status defined as no mutation on a Clinical Laboratory Improvement Amendments (CLIA)-certified next-generation sequencing (NGS) assay that has sequenced the full length TP53 gene. Patients can be enrolled based on tissue testing or liquid biopsies. If enrolled based on liquid biopsies, testing should have detected other somatic mutations. 2. Expansion cohort A only: estrogen receptor (ER) positive (\> 1%), human epidermal growth factor 2 (HER2) negative, WT TP53 metastatic or inoperable locally advanced or locally recurrent breast cancer regardless of progresterone receptor (PR) status, HER2 status will be defined according to the ASCO/CAP 2018 recommendationa (Patients can be HER2 0+ or 1+ by immunohistochemistry (IHC), 2+ by IHC and fluorescent in situ hybridization (FISH) non-amplified to be considered HER2 negative). Standard treatment with therapies known to confer a survival benefit does not exist, is no longer effective or tolerated, or the patient declines standard treatment. For the dose expansion cohort only, breast cancer patients with ER+, HER2- status must have received prior endocrine therapy and CDK4/6 inhibitors 3. Expansion cohort B only: advanced or metastatic solid tumors with MDM2 or MDM4 amplifications and WT TP53 metastatic for which standard treatment with therapies known to confer a survival benefit does not exist, is no longer effective or tolerated, or the patient declines standard treatment. 3. Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1. In the dose escalation stage, patients without measurable disease by RECIST 1.1, but evaluable disease are also eligible. 4. Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 (see Section 12, Appendix A). 5. Demonstrate adequate organ function as defined by the parameters listed below: 1. Serum creatinine ≤ 1.5 x upper limit of normal (ULN) or ≥ 45 mL/min/1.73m2 by CKD-EPI equation for subjects with creatinine levels \> 1.5 x institutional ULN. 2. Total bilirubin ≤ 1.5 x ULN, or direct bilirubin ≤ ULN for subjects with total bilirubin levels \> 1.5 x ULN, or unless due to Gilbert's Syndrome. 3. Alanine aminotransferase (ALT)/ aspartate aminotransferase (AST) ≤ 2.5 x ULN or ≤ 5 x ULN if hepatic abnormalities are related to underlying liver metastases or liver/biliary primary. 4. Absolute neutrophil count (ANC) ≥1500/mm3(without G-CSF in the 2 weeks prior to treatment start) 5. Platelet count ≥ 100,000/mm3 6. Hemoglobin ≥ 9 g/dL (without blood transfusion in the 2 weeks prior to treatment start) 6. All patients (males and females) of childbearing potential must agree to use medically effective contraception during the study and for 6 months after the last dose of study drugs. A negative urine or serum pregnancy test in women of childbearing potential is required within 72 hours prior to first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. 7. Have no concomitant medical condition (including, but not limited to, ongoing or active infection or any psychiatric disorder), that in the judgment of the investigator will interfere with the patient's ability to participate in the study or render such participation medically inappropriate. 8. No medical history of another cancer (except basal or squamous cell skin cancer or in situ cervical cancer, or carcinomas in situ or other malignancies with a ≥95% 5-year survival) within 2 years of the start of study treatment. 9. No investigational drug or other anticancer treatments (including chemotherapy or radiation, except palliative radiation) within 21 days or at least 5 half-lives, whichever is shorter, of the start of the study treatment. No palliative radiation within 2 weeks prior to the start of the study treatment. Supportive treatments such as LHRH agonists can be continued for patients with castration-resistant prostate cancer or pre-menopausal breast cancer while on treatment. 10. No major surgery within 1 month of treatment and fully recovered. 11. Willing and able to provide informed consent. Exclusion Criteria: An individual who meets any of the following criteria will be excluded from participation in this study: 1. Previous treatment with investigational agents that inhibit MDM2 or MDMX activity. 2. Known active hepatitis B, hepatitis C and/or human immunodeficiency virus (HIV)-positive patients who have a cluster of differentiation 4 (CD4) count \< 200. No antiretroviral medications that are CYP3A4 substrates will be allowed. 3. Pre-existing history of or known cardiovascular risk: 1. History of acute coronary syndromes within 6 months prior to the first dose of ALRN-6924 (including myocardial infarction, unstable angina, coronary artery bypass graft, angioplasty, or stenting). 2. Uncontrolled hypertension 3. Pre-existing cardiac failure (New York Heart Association class III-IV) 4. Clinically significant uncontrolled arrhythmias 5. Corrected QTcF interval on screening ECG ≥450 msec for males and ≥470 msec for females (QTcF \>480 msec for any patient with a bundle branch block). 4. Clinically significant gastrointestinal bleeding within 6 months prior to the start of study treatment. 5. Females who are pregnant or nursing. 6. Symptomatic central nervous system (CNS) metastases by history, clinical signs or radiologic findings. Patients with previously treated brain metastases are eligible if clinically stable and off steroid treatment for 2 weeks prior to study enrollment. Patients with new or progressive brain metastases (active brain metastases) are eligible if the treating physician determines that immediate CNS specific treatment is not required. 7. Known hypersensitivity to any study drug component. 8. The required use of any concomitant medications that are predominantly cleared by hepatobiliary transporters, OATP members OATP1B1 and OATP1B3, on the day of the ALRN-6924 infusion or within 48 hours after an ALRN-6924 infusion. 9. Patients with Grade ≥2 neuropathy will be excluded. 10. Patients with a known Human Papilloma Virus (HPV)-positive malignancy will be excluded from enrollment. This is owing to the fact that HPV-infected tumor cells continue to express the viral E6 protein, which is known to cause degradation of p53, hence rendering the expected ALRN-6924 - mediated dual inhibition of MDM2/MDMX very unlikely to restore p53 function.