The disclosure provides, in various embodiments, polynucleotides and vectors comprising sequences encoding a mono-specific or a bi-specific CAR that is capable of binding to a first TAA, or a T-cell engager that is capable of binding to CD3 and a second TAA, or a combination thereof. The disclosure also provides, in various embodiments, T lymphocytes comprising one or more of the polynucleotides or vectors; compositions (e.g., pharmaceutical compositions) and kits comprising one or more of the T lymphocytes; methods of treating a cancer in mammalian subject (e.g., a human), and methods of inducing T cell-mediated cytolysis of cancer cells (e.g., solid tumor cells).