The invention provides method of depleting endogenous T-cells or NK-cells to facilitate propagation or survival of engineered T-cells introduced into a subject for a therapeutic purpose. The depletion regime involves a co-administration of an immunotherapeutic agent against T-cells and an immunotherapeutic agent that inhibits CD47 interaction with NK-cells. The immunotherapeutic agent against T-cells or NK-cells binds to an antigen on T-cells or NK- cells effecting depletion of the T-cells or NK-cells, which depletion is promoted by the immunotherapeutic agent inhibiting CD47-SIRPα interaction. The genetically engineered T-cells or NK-cells can have a variety of genetic modifications such as a chimeric antigen receptor that targets the T-cells to a target cell.
