Both plants and animals rely on nucleotide-binding domain and leucine-rich repeat-containing (NB-LRR or NLR) proteins 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 AVR3a^EM isoform of the effector while retaining recognition of AVR3a^KI. Each one of eight single amino acid mutations is sufficient to expand the R3a response to AVR3a^EM 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 AVR3a^KI. Remarkably, the N336Y mutation, near the R3a nucleotide-binding pocket, conferred response to the effector protein PcAVR3a4 from the vegetable pathogen P. 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.