The goal of this study is to test A2B395, an allogeneic logic-gated Tmod CAR T-cell product in subjects with solid tumors including colorectal cancer (CRC), non-small cell lung cancer (NSCLC), head and neck squamous cell carcinoma (HNSCC), triple-negative breast cancer (TNBC), renal cell carcinoma (RCC) and other solid tumors that express EGFR and have lost HLA-A\*02 expression.

The main questions this study aims to answer are:

* Phase 1: What is the recommended dose of A2B395 that is safe for patients
* Phase 2: Does the recommended dose of A2B395 kill the solid tumor cells and protect the patient's healthy cells

Participants will be required to perform study procedures and assessments, and will also receive the following study treatments:

* Enrollment in BASECAMP-1 (NCT04981119)
* Preconditioning lymphodepletion (PCLD) regimen
* A2B395 Tmod CAR T cells at the assigned dose