Both plants and animals rely on nucleotide-binding domain and leucine-rich repeat-containing proteins (NB-LRRs or NLRs) to respond to invading pathogens and activate immune responses. How plant NB-LRR proteins respond to pathogens is poorly understood. We undertook a gain-of-function random mutagenesis screen of the potato NB-LRR immune receptor R3a to study how this protein responds to the effector protein AVR3a from the oomycete pathogen Phytophthora infestans. R3a response can be extended to the stealthy AVR3aEM isoform of the effector while retaining recognition of AVR3aKI. Each one of 8 single amino acid mutations is sufficient to expand the R3a response to AVR3aEM and other AVR3a variants. These mutations occur across the R3a protein, from the N-terminus to different regions of the LRR domain. Further characterization of these R3a mutants revealed that at least one of them was sensitized, exhibiting a stronger response than the wild-type R3a protein to AVR3aKI. Remarkably, the N336Y mutation, near the R3a nucleotide-binding pocket, conferred response to the effector protein PcAVR3a4 from the vegetable pathogen Phytophthora capsici. This work contributes to understanding how NB-LRR receptor specificity can be modulated. Together with knowledge of pathogen effector diversity, this strategy can be exploited to develop synthetic immune receptors.