A bi-phasic ternary Ag–In–Ga ink that demonstrates high electrical conductivity, extreme stretchability, and low electromechanical gauge factor (GF) is introduced. Unlike popular liquid metal alloys such as eutectic gallium–indium (EGaIn), this ink is easily printable and nonsmearing and bonds strongly to a variety of substrates. Using this ink and a simple extrusion printer, the ability to perform direct writing of ultrathin, multi-layer circuits that are highly stretchable (max. strain >600%), have excellent conductivity (7.02 × 105 S m–1), and exhibit only a modest GF (0.9) related to the ratio of percent increase in trace resistance with mechanical strain is demonstrated. The ink is synthesized by mixing optimized quantities of EGaIn, Ag microflakes, and styrene-isoprene block copolymers, which functions as a hyperelastic binder. When compared to the same composite without EGaIn, the Ag–In–Ga ink shows over 1 order of magnitude larger conductivity, up to ∼27× lower GF, and ∼5× greater maximum stretchability. No significant change over the resistance of the ink was observed after 1000 strain cycles. Microscopic analysis shows that mixing EGaIn and Ag microflakes promotes the formation of AgIn2 microparticles, resulting in a cohesive bi-phasic ink. The ink can be sintered at room temperature, making it compatible with many heat-sensitive substrates. Additionally, utilizing a simple commercial extrusion based printer, the ability to perform stencil-free, digital printing of multi-layer stretchable circuits over various substrates, including medical wound-dressing adhesives, is demonstrated for the first time.