Inclusion Criteria:
1. Written (signed and dated) informed consent and capable of co-operating with investigational medicinal product administration and follow-up.
2. Phase 1, dose escalation phase
Part A (HTL0039732 monotherapy):
* Histologically or cytologically proven advanced solid tumour, refractory to conventional treatment, or for which no further conventional therapy is considered appropriate by the Investigator or is declined by the potential participant.
* At least 1 measurable lesion according to RECIST v1.1, which (in the Investigator's opinion) has had objective radiological progression on or after the last therapy, or at least one assessable lesion e.g. pleural or peritoneal thickening that does not fulfil RECIST v1.1 criteria for measurable disease.
a. Consent for fresh tumour biopsy sample(s) at time of PD, if the participant has accessible disease and is eligible to receive atezolizumab. Optional at time of disease progression.
* Consent to access and analysis of any available archival tissue or a fresh tumour sample at baseline, if archival tissue is unavailable.
* Consent for fresh tumour biopsy sample(s) at time of PD, if the participant has accessible disease and is eligible to receive atezolizumab. Optional at time of disease progression.
Phase 1 Part B:
\- Histologically proven advanced solid tumour where PGE2/EP4 signalling is believed to be more prevalent or significant (such as microsatellite stable colorectal cancer (MSS CRC), gastro-esophageal cancer, head and neck squamous cell carcinoma (HNSCC), mCRPC, pancreatic cancer, lung cancer, bladder cancer, mesothelioma, cervical cancer, renal cancer, sarcoma, pheochromocytoma and cancers with PI3K/AKT/mTOR pathway activating mutations using a clinically-validated assay).
Phase 2a:
\- Histologically proven advanced solid tumour, in line with indications listed below, refractory to conventional treatment, or for which no conventional therapy is considered appropriate by the Investigator or is declined by the potential participant:
1. MSS CRC with PIK3CA or HER2 mutation, and/or other driver mutation as agreed with the Sponsor (genomic alteration to have been previously identified using a validated next-generation sequencing method performed on either tumour tissue or circulating tumour DNA \[ctDNA\]);
2. Gastric or gastroesophageal junction (GOJ) adenocarcinoma;
3. Clear cell renal cell carcinoma;
4. mCRPC
Phase 1 Part B and Phase 2a:
* Consent to access and analysis of any available archival tissue.
* Consent for fresh tumour biopsy samples at baseline and on treatment. However, the following exceptions will be permitted if archival tissue is available at the recruiting site:
1. Patients with mCRPC: biopsies are not required for those whose only safely accessible lesions are bone metastases that lack an accessible soft tissue component.
2. For the first 12 participants in each indication: the on-trial biopsy is optional; and the baseline biopsy is mandatory if there is a safely accessible lesion but may be omitted for patients who have no safely accessible lesion, to permit their inclusion in the study. This will continually be assessed through the study.
* Disease refractory to conventional treatment, or for which no further conventional therapy is considered appropriate by the Investigator or is declined by the participant.
* Except for mCRPC, at least 1 measurable lesion according to RECIST v1.1, which (in the Investigator's opinion) has had objective radiological progression on or after the last therapy. Potential participants with mCRPC may instead have had PD according to PCWG3 criteria.
1. Previously irradiated lesions cannot be counted as target lesions unless clearly progressed after the radiotherapy.
2. Lesions that are intended to be biopsied should not be counted as target lesions (those undergoing biopsy must have at least one target lesion that is not intended to be biopsied).
* For indications where anti-PD-1/PD-L1 therapy is standard of care (such as clear cell renal cell carcinoma, or gastric or GOJ adenocarcinoma with elevated PD-L1 expression), patients must have received that therapy and must be considered to have had progressive disease by the Investigator either on, or within 6 months after, that treatment.
3. Life expectancy of at least 12 weeks.
4. Eastern Cooperative Oncology Group performance status of 0 or 1.
5. Haematological and biochemical indices within the protocol specified ranges.
6. Stable thyroid function tests. Stable doses of thyroxine replacement are permitted.
7. Aged 18 years or over at the time consent is given.
Exclusion Criteria:
1. Radiotherapy (except for palliative reasons), chemotherapy, non chemotherapy systemic anti-cancer therapy (apart from life-long hormone suppression such as luteinising hormone-releasing agents in participants with mCRPC) or investigational medicinal products during the 4 weeks prior to enrolment; or first dose of an immunotherapy during the previous 12 weeks before first dose of HTL0039732.
2. Ongoing toxic manifestations of previous treatments that are Grade \>1 per CTCAE v5.0.
3. Any central nervous system metastases (unless potential participants have had local therapy and are asymptomatic, radiologically stable and have been off steroids for ≥4 weeks prior to enrolment).
4. Women of child-bearing potential (or who are already pregnant or lactating). Exceptions apply.
5. Men with partners of childbearing potential. Exceptions apply.
6. Major thoracic or abdominal surgery from which the potential participant has not yet recovered.
7. At high medical risk because of non-malignant systemic disease, including active uncontrolled infection.
8. Known history of current or latent tuberculosis, HIV or Hepatitis B or C infection.
9. Prior treatment with EP4 inhibitor.
10. Treatment with selective cyclooxygenase-2 inhibitor in the 8 weeks prior to enrolment.
11. Known hypersensitivity or intolerance to hydroxypropyl methylcellulose.
12. Use of systemic immunosuppressive agent in the 2 weeks prior to enrolment. Exceptions apply.
13. Significant cardiovascular disease.
14. Known active peptic ulcer disease, or symptoms of gastritis, dyspepsia or gastro-esophageal reflux disease (one or more episodes per week).
15. Current or planned participation in another interventional clinical trial, whilst taking part in this trial of HTL0039732.
16. Limited ability to swallow or absorb oral medications.
17. Any other condition that, in the Investigator's opinion, would mean that the trial is not in the best interests of the potential participant.
Phase 1 Part B and Phase 2a:
18. Any live vaccines in the 4 weeks prior to enrolment.
19. Diagnosis of immunodeficiency.
20. Active autoimmune disease requiring systemic treatment in the 2 years prior to enrolment.
21. History or clinical suspicion of interstitial lung disease, history of (non-infectious) pneumonitis that required steroids, or current pneumonitis.
22. Hypersensitivity to atezolizumab or any of its excipients.
23. Prior adverse reaction to cancer immunotherapy that required steroid or other immunosuppressive treatment or led to discontinuation of that treatment.
