• Participants who have progressed on at least one previous regimen of anticancer therapy (chemotherapy, mutation targeted therapy, and/or CPI therapy)
• Measurable disease, as defined by RECIST Version 1.1
• Eastern Cooperative Oncology Group (ECOG) Performance Status 0 or 1 or Karnofsky Performance Score greater than or equal to (>=) 70
• Life expectancy of >=12 weeks
• Confirmed at least one tumor lesion with location accessible to safely biopsy per clinical judgment of the treating physician.

Biopsies are not applicable to participants in Cohorts G, H, K, and L presenting with a single target lesion and absence of any non-target lesion.

• Consent to provide an archival tumor tissue sample (if available, applicable to all participants)
• Willingness to undergo baseline and on-treatment tumor biopsies for pharmacodynamics (PD) biomarker analysis (biopsies are optional for Cohort A)
• Adequate cardiovascular function as defined in the study protocol
• AEs related to any previous radiotherapy, chemotherapy, or surgical procedure must have resolved to Grade less than or equal to (<=) 1, except alopecia (any grade) and Grade 2 peripheral neuropathy
• Adequate haematological, liver, and renal functions.
• Participants with unilateral pleural effusion (indications other than NSCLC) are eligible if they fulfill both of the following:
• NYHA Class 1 2. Forced expiratory volume 1 (FEV1) and forced vital capacity (FVC) >70% of predicted value; participants with lung metastases should present with DLCO >60% of predicted value.
• Participants with Gilbert's syndrome will be eligible for the study
• Participants must have had confirmed diagnosis of recurrent or metastatic squamous cell carcinoma head and neck, or esophageal cancer or metastatic, persistent or recurrent squamous cervical cancer.

• Symptomatic or untreated central nervous system (CNS) metastases
• History of treated asymptomatic CNS metastases as described in the protocol
• Spinal cord compression not definitively treated with surgery and/or radiation or previously diagnosed and treated spinal cord compression without evidence that disease has been clinically stable for >=2 weeks before enrollment
• Leptomeningeal disease
• An active second malignancy
• Penetrating tumor infiltration
• Evidence of significant, uncontrolled concomitant diseases that could affect compliance with the protocol or interpretation of results
• Episode of significant cardiovascular/cerebrovascular acute disease within 6 months before study treatment administration
• History of significant vascular disease (for example, aortic aneurysm, aortic dissection)
• Active or uncontrolled infections
• Human immunodeficiency virus (HIV) or Active Hepatitis A, B, C, D or E infection (HAV/HBV/HCV/HDV/HEV).
• Severe infection within 4 weeks before study treatment administration including, but not limited to, hospitalization for complications of infection, bacteremia, or severe pneumonia.
• History of chronic liver disease or evidence of hepatic cirrhosis
• Dementia or altered mental status that would prohibit informed consent
• History of, active or suspicion of autoimmune disease
• History of idiopathic pulmonary fibrosis, pneumonitis (including drug-induced), organizing pneumonia (bronchiolitis obliterans, cryptogenic organizing pneumonia, etc.), or evidence of active pneumonitis on screening chest computed tomography (CT) scan. History of radiation pneumonitis in the radiation field (fibrosis) is permitted
• Bilateral pleural effusion confirmed by X-ray
• Any other diseases, metabolic dysfunction, physical examination finding, or clinical laboratory finding that give reasonable suspicion of a disease or condition that would contraindicate the use of an investigational drug
• Concurrent therapy with any other investigational drug
• Immunomodulating agents as described in study protocol
• Chronic use of steroids
• Last dose with any cytostatic treatments < 28 days before study treatment administration
• Radiotherapy within the last 4 weeks before start of study treatment administration, with the exception of limited field palliative radiotherapy
• Administration of a live, attenuated vaccine within 4 weeks before Cycle 1 Day 1 or at any time during the study and 5 months after the last dose of atezolizumab
• Major surgery or significant traumatic injury <28 days before study treatment administration (excluding fine needle biopsies) or if wound healing has not completed after surgery or anticipation of the need for major surgery during study treatment
• Known hypersensitivity to any of the components of the simlukafusp alfa drug product or atezolizumab drug product
• Severe dyspnea at rest or requiring supplementary oxygen therapy Locally curative options are available for participant's disease.