Inclusion Criteria:

          -  18 years of age or older

          -  Histologically- or cytologically-confirmed solid tumors (excluding lymphomas) that are
             metastatic or unresectable and that meet the following criteria: a) 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; b) Expansion cohort 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.
             Patients can be HER2 0+ or 1+, 2+ or 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.

          -  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.

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0-1.

          -  Serum creatinine =< 1.5 x upper limit of normal (ULN) or >= 45 mL/min/1.73 m^2 by
             Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation for subjects with
             creatinine levels > 1.5 x institutional ULN.

          -  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.

          -  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.

          -  Absolute neutrophil count (ANC) >=1500/mm^3 (without granulocyte-colony stimulating
             factor [GCSF] in the 2 weeks prior to treatment start).

          -  Platelet count >= 100,000/mm^3.

          -  Hemoglobin >= 9 g/dL (without blood transfusion in the 2 weeks prior to treatment
             start).

          -  International normalized ratio (INR) and activated partial thromboplastin time (aPTT)
             =< 1.5 x ULN.

          -  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. Females must have a negative serum pregnancy test during screening and a
             negative urine pregnancy test at study day 1 prior to initiation of treatment.

          -  Have no concomitant medical condition 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.

          -  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.

          -  No investigational drug or other anticancer treatments (including chemotherapy or
             radiation therapy) within 21 days or at least 5 half-lives, whichever is shorter, of
             the start of the study treatment.

          -  No major surgery within 1 month of treatment and fully recovered.

          -  Willing and able to provide informed consent.

        Exclusion Criteria:

          -  Previous treatment with investigational agents that inhibit MDM2 or MDMX activity.

          -  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.

          -  Requirement for therapeutic anticoagulation.

          -  Pre-existing history of or known cardiovascular risk: a) 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);
             b) Uncontrolled hypertension; c) Pre-existing cardiac failure (New York Heart
             Association class III-IV); d) Atrial fibrillation on anti-coagulants; e) Clinically
             significant uncontrolled arrhythmias; f) Corrected QTcF interval on screening
             electrocardiography (ECG) >= 450 msec for males and >= 470 msec for females (QTcF >
             480 msec for any patient with a bundle branch block).

          -  Clinically significant gastrointestinal bleeding within 6 months prior to the start of
             study treatment.

          -  Females who are pregnant or nursing.

          -  Symptomatic central nervous system (CNS) metastases by history, clinical signs or
             radiologic findings. Stable brain metastases (1 month after completion of treatment)
             confirmed by imaging are allowed.

          -  Known hypersensitivity to any study drug component.

          -  The required use of any concomitant medications that are predominantly cleared by
             hepatobiliary transporters, Organic-anion-transporting polypeptide (OATP) members
             OATP1B1 and OATP1B3, on the day of the ALRN-6924 infusion or within 48 hours after an
             ALRN-6924 infusion.

          -  Patients with grade >= 2 neuropathy will be excluded.