Core Inclusion Criteria:
1. ECOG performance status 0 or 1 with no deterioration over the previous 2 weeks
2. Estimated life expectancy of greater than 12 weeks
3. Ability to swallow and retain oral medication
4. Women either of non-childbearing potential or of childbearing potential willing to practice effective contraception for the duration of the study and for 6 months (Module 1, Module 4) and 24 months (Module 2) after the last dose of CT7001
5. Sexually active male patients must be willing to use condoms with all sexual partners for the duration of the study and for 3 months after the last dose of CT7001.
6. Provision of signed and dated, written informed consent
Core Exclusion Criteria:
1. Any other malignancy that has been active or treated within the past 3 years, with the exception of cervical intraepithelial neoplasia and non-melanoma skin cancer
2. Any unresolved toxicity (except alopecia) from prior therapy of ≥ CTCAE Grade 2
3. Spinal cord compression or brain metastases, unless asymptomatic, stable, and not requiring steroids for at least 4 weeks before the first dose of investigational product (IP)
4. Refractory nausea and vomiting, chronic gastrointestinal (GI) disease or previous significant bowel resection, with clinically significant sequelae that would preclude adequate absorption of CT7001
5. Uncontrolled seizures
6. Active infection requiring systemic antibiotic, antifungal, or antiviral medication
7. Severe or uncontrolled medical condition or psychiatric condition
8. Active bleeding diatheses
9. Renal transplant
10. Known hepatitis B, hepatitis C, or human immunodeficiency virus infection
11. Breastfeeding or pregnancy
12. Receipt of systemic cytotoxic treatment for the malignancy within 28 days or ≤ 5 half-lives, whichever is shorter before the first dose of IP
13. Receipt of non-cytotoxic treatment for the malignancy within 5 half-lives of the drug before the first dose of IP
14. Receipt of corticosteroids (at a dose \> 10 mg prednisone/day or equivalent) within 14 days before the first dose of IP
15. Receipt of any small-molecule investigational medicinal product (IMP) within 28 days or ≤ 5 half-lives, whichever is shorter before the first dose of IP
16. Receipt of any biological IMP (e.g., immune checkpoint blockers, antibodies, nanoparticles) within 42 days before the first dose of IP
17. Receipt of St John's Wort within 21 days before the first dose of IP or of another concomitant medication, herbal supplement, or food that is a strong inhibitor or inducer of CYP3A4, CYP2C19, CYP2D6, or P-glycoprotein (PGP) activity within 14 days before the first dose of CT7001
18. Receipt of a blood transfusion (blood or blood products) within 14 days before the first dose of IP
19. Known hypersensitivity to CT7001 or any excipient of the product
20. Impaired hepatic or renal function as demonstrated by any of the following laboratory values:
1. Albumin \< 30 g/L
2. Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) \> 2.5 × the upper limit of normal (ULN)
3. \> 5.0 × ULN for patients with liver metastases
4. Total bilirubin \> 1.5 × ULN
5. Serum creatinine \> 1.5 × ULN
21. Liver function deteriorating in a manner that would likely make the participant meet the AST, ALT, or bilirubin levels specified above at the time of the first dose of IP
22. Other evidence of impaired hepatic synthesis function
23. Inadequate bone marrow reserve or organ function as demonstrated by any of the following laboratory values:
1. Absolute neutrophil count (ANC) \< 1.5 × 10\^9/L
2. Platelet count \< 100 × 10\^9/L
3. Haemoglobin \< 90 g/L
24. Persistent (\> 4 weeks) severe pancytopenia due to previous therapy rather than to disease (ANC \< 0.5 × 10\^9/L or platelets \< 50 x 10\^9/L)
25. Cardiac dysfunction (defined as myocardial infarction within 6 months of study entry, New York Heart Association Class II/III/IV heart failure, unstable angina, unstable cardiac arrhythmias, or left ventricular ejection fraction \< 55 percent)
26. Mean resting QT interval corrected for heart rate by the Fridericia formula (QTcF) \> 470 msec obtained from 3 electrocardiograms (ECGs) obtained within 5 minutes of each other prior to the first dose
27. Any clinically important abnormalities in rhythm, conduction, or morphology on resting ECG (e.g., complete left bundle branch block, third degree heart block). Controlled atrial fibrillation (AF) is permitted
28. Any factor that increases the risk of QTc prolongation or of arrhythmic events (e.g., heart failure, hypokalaemia, congenital long QT syndrome, immediate family history of long QT syndrome or unexplained sudden death under 40 years of age)
29. In the opinion of the Investigator, unlikely to comply with study procedures, restrictions, or requirements
30. A history of haemolytic anaemia or marrow aplasia
31. Has received a live-virus vaccination within 28 days or less of planned treatment start
Additional Module 1A Inclusion Criteria:
1. Histological, radiological or cytological confirmation of an advanced non-haematological malignancy not considered to be appropriate for further standard treatment
2. Module 1A biopsy cohort only : at least one tumour suitable for repeat biopsy
Additional Module 1A Exclusion Criteria:
1\. International normalised ratio (INR) ≥1.5
Additional Module 1B Inclusion Criteria
1. Histological or cytological confirmation of metastasis or locally advanced tumour
2. At least one line of systemic anti-cancer therapy
3. Disease measurable by RECIST v1.1
Additional Module 1B-1 (TNBC Expansion) Inclusion Criteria:
1. Histologically-confirmed carcinoma of breast not expressing oestrogen receptor (ER) or progesterone receptor (PR) and negative for human epidermal growth factor receptor 2 (HER2)
2. Documented disease progression on or within 6 months of most recent cytotoxic prior cytotoxic chemotherapy
3. Disease measurable by RECIST v1.1
4. Must have received at least one cytotoxic chemotherapy for metastatic/locally advanced disease
Additional Module 1B-1 (TNBC Expansion) Exclusion Criteria:
1. No more than three lines of cytotoxic chemotherapy for metastatic/locally advanced disease
2. No advanced, symptomatic visceral metastases
3. No known symptomatic central nervous system (CNS) metastases, carcinomatous meningitis or leptomeningeal disease
4. Prior exposure to CT7001
5. Patients who are investigational site staff members directly involved in the conduct of the trial and their family members, site staff members otherwise supervised by the Investigator, or patients who are Carrick employees directly involved in the conduct of the trial
Additional Module 2A Inclusion Criteria:
1. Women only
2. Pre- or peri-menopausal women must have initiated LHRHa at least 28 days prior to first dose of CT7001/placebo
3. Histologically-confirmed, metastatic or locally advanced, ER+ve and/or PGR+ve and HER2-ve breast cancer
4. Disease measurable by RECIST v1.1
5. Documented objective disease progression while on, or within 6 months after the end of, the most recent therapy
6. Must have received an aromatase inhibitor together with a CDK4/6 inhibitor in the same line of therapy for locally advanced or metastatic disease or for treatment of early breast cancer if the disease-free interval was \<12 months.
7. Ability to receive intramuscular injections.
Additional Module 2A Exclusion Criteria:
1. Prior therapy with fulvestrant
2. More than 2 lines of endocrine treatment for locally advanced or metastatic disease
3. Prior treatment with more than one line of cytotoxic chemotherapy for locally advanced or metastatic breast cancer.
4. Patients with liver metastasis will be limited to approximately 30-40% of the enrolled patients. l
5. Known hypersensitivity to CT7001, fulvestrant or any excipient of the investigational products
6. Patients who are investigational site staff members directly involved in the conduct of the trial and their family members, site staff members otherwise supervised by the Investigator, or patients who are Carrick employees directly involved in the conduct of the trial
Additional Module 4 Inclusion Criteria:
1. Patients must be able to eat a high-fat meal, as provided by the study site, within a 30-minute period
2. Histological, radiological or cytological confirmation of an advanced non-haematological malignancy not considered to be appropriate for further standard treatment
Additional Module 4 Exclusion Criteria:
1\. Patients who were unable to fast for at least 10 hours
