Study of an Anti-HER3 Antibody, HMBD-001, With Docetaxel +/- Cetuximab in Advanced Squamous Non-small Cell Lung Cancers, and HMBD-001 + Cetuximab in Advanced Squamous Cell Cancers

Inclusion Criteria:

* Ability to understand and be willing to sign an informed consent form

1. Males and females aged over 18 years (or having reached the age of majority according to local laws if the age of majority is > 18 years of age)
2. Eastern Cooperative Oncology Group (ECOG) status of 0 to 1
3. Arm B only: Locally advanced or metastatic squamous non-small cell lung cancer for which all available standard of care treatment options have been exhausted or refused and for which at least one lesion is measurable
4. Arm C only: Advanced or metastatic sqNSCLC, HNSCC, ESCC, CSCC or cervical SCC with at least one prior line of systemic therapy,
5. Have an estimated life expectancy of at least 3 months
6. Participants must be willing to provide a fresh tumor biopsy sample
7. Have adequate organ function
8. Females must be non-pregnant and non-lactating, willing to use a highly effective method of contraception from screening until study completion or be either surgically sterile or post-menopausal
9. Males must be surgically sterile, abstinent, or if engaged in sexual relations with a woman of child-bearing potential, the participant and his partner must be surgically sterile or using an acceptable, highly effective contraceptive method from screening until study completion

Exclusion Criteria:

* Prior treatment with HMBD-001, docetaxel, cetuximab or any other agent that targets Epidermal Growth Factor Receptor (EGFR) or HER3, including pan-HER inhibitors. Prior treatment with docetaxel is allowed for Arm C

1. Receipt of prior targeted therapy, including but not limited to those targeting EGFR activating mutations, ALK fusions, ROS rearrangements, RET fusions or mutations, BRAF V600E mutation, MET exon 14 skipping mutation, and/or KRAS G12C mutation
2. Persistent clinically significant toxicities (Grade ≥2) from previous anti-cancer therapy except for Grade >2 toxicities that are considered unlikely to put the participant at an increased risk of treatment-related toxicity and/or impact the study results e.g., alopecia
3. Most recent anti-cancer therapy including radiotherapy at least 4 weeks, or nitrosourea or mitomycin 3 at least 6 weeks, or 5 half-lives whichever is shorter prior to starting the assigned study treatment
4. Symptomatic primary Central Nervous System (CNS) cancer or metastases unless the symptoms are stable for at least 28 days prior to the first dose of the study drug and any symptoms have returned to baseline
5. Evidence of abnormal cardiac function
6. History of uncontrolled allergic reactions and/or known expected hypersensitivity to the study drugs used in the treatment arm to which the participant is to be enrolled into
7. Any other known active malignancy except for treated cervical intraepithelial neoplasia, or non-melanoma skin cancer
8. Any uncontrolled illness or significant uncontrolled condition(s) requiring systemic treatment
9. Known Human Immunodeficiency Virus (HIV) infection
10. Active hepatitis B or hepatitis C infection
11. Pregnant or breast feeding
12. COVID 19 infection within 3 months prior to the first dose of the study drug
13. COVID 19 vaccination within 14 days prior to the first dose of the study drug
14. Treatment with strong inhibitors or inducers of CYP3A4