Patient description: The patient is a 37-year-old woman who came to the clinic for a routine Pap smear. The test revealed stage 1B of cervical cancer. The patient tested positive for HPV 16. She has three sexual partners and four children. She underwent tubal ligation. She smokes 30 packs/year and drinks alcohol frequently. She is otherwise healthy. She was offered a radical hysterectomy.

Clinical trial eligibility criteria: eligible ages (years): 18.0-999.0,  Advanced Breast Carcinoma Advanced Colorectal Carcinoma Advanced Gastroesophageal Junction Adenocarcinoma Advanced Malignant Solid Neoplasm Anatomic Stage III Breast Cancer AJCC v8 Anatomic Stage IIIA Breast Cancer AJCC v8 Anatomic Stage IIIB Breast Cancer AJCC v8 Anatomic Stage IIIC Breast Cancer AJCC v8 Anatomic Stage IV Breast Cancer AJCC v8 Clinical Stage III Gastroesophageal Junction Adenocarcinoma AJCC v8 Clinical Stage IV Gastroesophageal Junction Adenocarcinoma AJCC v8 Clinical Stage IVA Gastroesophageal Junction Adenocarcinoma AJCC v8 Clinical Stage IVB Gastroesophageal Junction Adenocarcinoma AJCC v8 HER2 Positive Breast Carcinoma Metastatic Breast Carcinoma Metastatic Gastroesophageal Junction Adenocarcinoma Metastatic Malignant Solid Neoplasm Pathologic Stage III Gastroesophageal Junction Adenocarcinoma AJCC v8 Pathologic Stage IIIA Gastroesophageal Junction Adenocarcinoma AJCC v8 Pathologic Stage IIIB Gastroesophageal Junction Adenocarcinoma AJCC v8 Pathologic Stage IV Gastroesophageal Junction Adenocarcinoma AJCC v8 Pathologic Stage IVA Gastroesophageal Junction Adenocarcinoma AJCC v8 Pathologic Stage IVB Gastroesophageal Junction Adenocarcinoma AJCC v8 Prognostic Stage III Breast Cancer AJCC v8 Prognostic Stage IIIA Breast Cancer AJCC v8 Prognostic Stage IIIB Breast Cancer AJCC v8 Prognostic Stage IIIC Breast Cancer AJCC v8 Prognostic Stage IV Breast Cancer AJCC v8 Stage III Colorectal Cancer AJCC v8 Stage IIIA Colorectal Cancer AJCC v8 Stage IIIB Colorectal Cancer AJCC v8 Stage IIIC Colorectal Cancer AJCC v8 Stage IV Colorectal Cancer AJCC v8 Stage IVA Colorectal Cancer AJCC v8 Stage IVB Colorectal Cancer AJCC v8 Stage IVC Colorectal Cancer AJCC v8 Unresectable Colorectal Carcinoma Unresectable Gastroesophageal Junction Adenocarcinoma Unresectable Malignant Solid Neoplasm DOSE-ESCALATION PHASE: Must have histologically confirmed advanced solid tumor DOSE-EXPANSION PHASE: Must have histologically confirmed advanced/metastatic gastroesophageal cancer (cohort A) or colorectal cancer (cohort B) DOSE-EXPANSION PHASE: Patients must have a biopsiable lesion and provide consent for on treatment biopsy Age >=18 years. Because no dosing or adverse event data are currently available on the use of AZD6738 in combination with DS-8201a in patients < 18 years of age, children are excluded from this study Patients must have HER2-positive or HER2-expressing tumors determined by a Clinical Laboratory Improvement Act (CLIA)-certified laboratory. As a rule, for HER2 immunohistochemistry (IHC) scoring system trastuzumab for gastric cancer (TOGA) used for gastric/gastroesophageal junction (GEJ) cancers will be employed (Note: in escalation phase, for breast cancer patients that are included, breast cancer can be used). Specific requirement of HER2 status is outlined below HER2 expression (1-3+) by IHC locally and confirmed centrally OR HER2 expression (1-3+) by IHC tested centrally OR HER2 amplification based on fluorescence in situ hybridization (FISH) or next generation sequencing Must have received at least one line of systemic chemotherapy for either locally advanced or metastatic disease and should have either progressed on this therapy or been intolerant to this therapy For tumors where anti-HER2 therapy is standard of care, patients must have progressed on at least 1 line of anti-HER2 therapy if eligible  Patients with a history of (non-infectious) interstitial lung disease (ILD)/pneumonitis that required steroids, have current ILD/pneumonitis, or where suspected ILD/pneumonitis cannot be ruled out by imaging at screening. Patient using e-cigarettes/vaping are also excluded Patients with a medical history of myocardial infarction within 6 months before enrollment (study treatment), symptomatic congestive heart failure (New York Heart Association Class II to IV, corrected QT interval (QTcF) prolongation to > 470 ms (females) or > 450 ms (males) as corrected by Framingham's formula Patients with spinal cord compression or clinically active central nervous system metastases, defined as untreated and symptomatic, or requiring therapy with corticosteroids or anticonvulsants to control associated symptoms Patients with multiple primary malignancies within 2 years, except adequately resected non-melanoma skin cancer, curatively treated in situ disease, or other curatively treated solid tumors Patients with a history of severe hypersensitivity reactions to either the drug substances or inactive ingredients in the drug product Patients with an uncontrolled infection requiring IV antibiotics, antivirals, or antifungals Patients with substance abuse or any other medical conditions that would increase the safety risk to the subject or interfere with participation of the subject or evaluation of the clinical study in the opinion of the investigator Patients with a concomitant medical condition that would increase the risk of toxicity in the opinion of the investigator Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities grade >1) with the exception of alopecia. Subjects with chronic grade 2 toxicities may be eligible per discretion of the investigator after discussion with study principal investigator (PI) (e.g., grade 2 chemo-induced neuropathy) Any previous treatment with an ATR inhibitor