The effects of BiMeO3 (Me=Fe, Sc, Mn, Al) addition on the phase transition and electrical properties of Bi0.5(Na0.80K0.20)0.5TiO3 (BNKT20) lead-free piezoceramics were systematically investigated. Results showed that addition of BiFeO3 into BNKT20 induces a phase transition from tetragonal-rhombohedral coexisted phases to a tetragonal phase with the observation of enhanced piezoelectric properties (d33=150pC/N for 0.02BiFeO3). BiScO3, BiMnO3, and BiAlO3 substitutions into BNKT20 induce a phase transition from coexistence of ferroelectric tetragonal and rhombohedral to a relaxor pseudocubic with a significant disruption of the long-range ferroelectric order, and correspondingly adjusts the ferroelectric-relaxor transition point TF-R to room temperature. Accordingly, large accompanying normalized strains of 0.34%-0.36% are obtained near the ferroelectric-relaxor phase boundary, and the mergence of large strain response can be ascribed to a reversible field-induced ergodic relaxor-to-ferroelectric phase transformation. Moreover, our study also revealed that the composition located at the ferroelectric-relaxor phase boundary where the strain response is consistently derivable shifts to a BNKT20-rich composition as the tolerance factor t of the end-member BiMeO3 increases, and this relationship is expected to provide a guideline for designing high-performance (Bi0.5Na0.5)TiO3-based materials by searching the ferroelectric-relaxor phase boundary.