Key Inclusion Criteria - Arms 1a, 1b, 2, and 3
* Participants must be ≥ 18 years of age.
* For Arm 1a only, locally advanced or metastatic (Stage IV) solid tumor that has progressed during or after standard therapy and for whom no available therapies are appropriate (based on the judgment of the Investigator).
* At least 1 measurable lesion per RECIST 1.1.
* Lesions previously treated with radiation or other forms of locoregional therapy must show radiographic evidence of disease progression to be used as a target lesion.
* For Arms 1a, 1b, and 2 only, washout period from the last dose of previous anticancer therapy (chemotherapy, biologic, or other investigational agent) to the initiation of study drug must be \> 5 times the half-life of the agent or \> 21 days (whichever is shorter).
* Resolution of non-immune-related AEs secondary to prior anticancer therapy (excluding alopecia and peripheral neuropathy) to ≤ Grade 1 per NCI-CTCAE version 5.0 or higher, and complete resolution of immune-related AEs secondary to prior checkpoint inhibitor therapy.
* Serum creatinine clearance ≥ 30 mL/min per Cockcroft-Gault formula.
* Total bilirubin ≤ 1.5 × ULN (≤ 3 × ULN if elevated because of liver metastases or documented Gilbert's syndrome).
* Aspartate aminotransferase/serum glutamic oxaloacetic transaminase (AST/SGOT) and alanine aminotransferase/serum glutamic pyruvic transaminase (ALT/SGPT) \< 2.5 × ULN or \< 5 × ULN for patients with known liver metastases.
* Adequate hematologic function, defined as absolute neutrophil count ≥ 1.0 × 10\^9/L, hemoglobin ≥ 8.0 g/dL, and platelet count ≥ 75 × 10\^9/L.
* Eastern Cooperative Oncology Group (ECOG) performance status 0-1.
* Ejection fraction ≥ 50%, as measured by echocardiogram, multigated acquisition scan, nuclear stress test, or equivalent modality.
* Willingness of male and female patients who are not surgically sterile or postmenopausal to use medically acceptable methods of birth control for the duration of the study treatment period, including 90 days after the last dose of CHS-114, 4 months after the last dose of toripalimab; male patients must refrain from donating sperm during this period. Sexually active men, and women using oral contraceptive pills, should also use barrier contraception. Azoospermic male patients and women of childbearing potential who are continuously not heterosexually active are exempt from contraceptive requirements.
Additional Inclusion Criteria - Arms 1b and 2 only
* Histologically or cytologically confirmed advanced or metastatic HNSCC that has progressed during or after a platinum-based chemotherapy and/or a programmed cell death receptor (PD)-1 or PD ligand 1 (PD-L1) targeting agent (separately or in combination therapy).
* Metastatic or locoregionally recurrent HNSCC malignancy that is incurable by surgery or radiotherapy.
* Arm 1b only, participants must have tumor tissue that is accessible for pretreatment and on-treatment tumor biopsy in the opinion of the Investigator and be willing and consent to undergo pretreatment and on-treatment biopsies per protocol.
Additional Inclusion Criteria - Arm 3 only
* Histologically or cytologically confirmed locally advanced or metastatic HNSCC (primary tumor location of oral cavity, oropharynx, hypopharynx, or larynx). Participants may not have a primary tumor site of nasopharynx (any histology).
* Participants should have been treated with anti-PD-1/PD-L1-directed systemic therapy for incurable recurrent, advanced, or metastatic disease and experienced progressive disease. targeting agent (separately or in combination therapy).
* Metastatic or locoregionally recurrent HNSCC malignancy that is incurable by surgery or radiotherapy.
* Consent to provide HPV status assessed by p16 and results from baseline PD-L1 IHC assay score.
* Consent to provide tumor tissue samples is required for enrollment.
Key Exclusion Criteria - Arms 1a, 1b, 2, and 3
* Previously received an anti-CCR8 antibody or anti-CCR8 targeted therapy.
* History of Grade 4 allergic or anaphylactic reaction to any monoclonal antibody therapy or any excipient in the study drugs.
* Major surgery within 4 weeks prior to Screening.
* Unstable or severe uncontrolled medical condition (eg, unstable cardiac function, unstable pulmonary condition including pneumonitis and/or interstitial lung disease, uncontrolled diabetes, symptomatic fistula) or any important medical illness or abnormal laboratory finding that would, in the Investigator's judgment, increase the risk to the patient associated with his or her participation in the study.
Additional Exclusion Criteria - Arms 1b and 2 only
* Received \> 4 prior systemic regimens for advanced/metastatic disease.
* Nasopharyngeal carcinoma or nasal cavity malignancies other than HNSCC (eg, adenocarcinoma and variants, neuroendocrine tumors, mucosal melanoma).
* Receiving chronic anti-coagulation therapy (eg, warfarin, enoxaparin) that cannot be safely discontinued temporarily for the required biopsies (only for patients who provide tumor biopsies).
Additional Exclusion Criteria - Arm 3
• Received ≥ 2 prior systemic regimens for advanced/metastatic disease.
