Programmed connection of amino acids or nucleotides into chains introduced a revolution in control of biological function. Reacting proteins together is more complex because of the number of reactive groups and delicate stability. Here we achieved sequence-programmed irreversible connection of protein units, forming polyprotein teams by sequential amidation and transamidation. SpyTag peptide is engineered to spontaneously form an isopeptide bond with SpyCatcher protein. By engineering the adhesin RrgA from Streptococcus pneumoniae, we developed the peptide SnoopTag, which formed a spontaneous isopeptide bond to its protein partner SnoopCatcher with >99% yield and no cross-reaction to SpyTag/SpyCatcher. Solid-phase attachment followed by sequential SpyTag or SnoopTag reaction between building-blocks enabled iterative extension. Linear, branched, and combinatorial polyproteins were synthesized, identifying optimal combinations of ligands against death receptors and growth factor receptors for cancer cell death signal activation. This simple and modular route to programmable “polyproteams” should enable exploration of a new area of biological space.