Core Inclusion Criteria:
* Histopathologically or cytologically confirmed diagnosis of malignant disease evaluable by RECIST v1.1
* Provision of signed written informed consent before any study-related activities, willing and able to comply with all scheduled visits, treatment plans, laboratory tests, and other study procedures and willing to permit access to stored historical tumor tissue, prior tumor radiological assessments and tumor biomarker data.
* ECOG performance status of ≤ 2 with no deterioration over the previous 2 weeks.
* Ability to take oral medications and be willing to record daily adherence to the study drug.
* Women either of non-childbearing potential, either confirmed to be post-menopausal or of childbearing potential willing to practice effective contraception for the duration of the study and for minimum 33 days after the last dose of CT7439.
* Sexually active male patients must be willing to refrain from sperm donation from the time of signing informed consent and use condoms with all sexual partners for the duration of the study and for a minimum 93 days months after the last dose of CT7439.
* Estimated life expectancy of at least 3 months, in the opinion of the investigator.
Core Exclusion Criteria:
* Prior therapy with a specific CDK12/13 inhibitor, within any timeframe prior to the first dose of CT7439.
* Participants with any other malignancy that have been active or treated within the past 3 years prior to enrolment, with the exception of cervical intraepithelial neoplasia and non-melanoma skin cancer.
* Any unresolved toxicity (except alopecia) from prior therapy of ≥ 2 Common Terminology Criteria for Adverse Events (CTCAE) Grade.
* Active or documented history of autoimmune disease.
* Any current or prior central nervous system metastases
* Active infection requiring systemic antibiotic, antifungal, or antiviral medication within 14 days prior to first dose of study drug.
* Severe or uncontrolled medical condition or psychiatric condition.
* Human immunodeficiency virus (HIV) infection, unless the study participant on anti-retroviral therapy for at least 4 weeks (28 days),and has not had an opportunistic infection within the past 12 months prior to enrollment.
* Active hepatitis B virus (HBV) or hepatitis C virus (HCV) infection, unless participant with HBV patient is on a suppressive antiviral therapy, or participant with HCV has a viral load below the limit of quantification (LoQ).
* Participant is breastfeeding or pregnant.
* Receipt of cytotoxic and/or non- cytotoxic treatment for the malignancy within 28 days before the first dose of IMP.
* Receipt of corticosteroids within 14 days before the first dose of IMP.
* Receipt of any small molecule IMP within 28 days or 5 half-lives, whichever is longer, before the first dose of IMP.
* Receipt of concomitant medication, herbal supplement, or food that is a moderate and/or strong inhibitor or inducer of CYP3A4,,strong inhibitor or inducer of CYP2D6 or P-gp or inhibitor of BCRP within 21 days before the first dose of IMP.
* Inadequate hepatic, renal and bone marrow function, receipt of a blood transfusion (blood or blood products) within 14 days before the first dose of IMP.
* Persistent (\> 4 weeks) severe pancytopenia due to previous therapy rather than to disease (ANC \< 0.5 × 109/L or platelets \< 50 x 109/L).
* History of cardiac dysfunction and/or presence of clinically significant cardiovascular disease
* Has received a live virus vaccination within 28 days or less of planned treatment start.
Additional Module 1 inclusion criteria:
1\. Clinically confirmed locally advanced or metastatic solid malignancy for which there is no potentially curative treatment option.
