We report the discovery of KMT-2020-BLG-0414Lb, with a planet-to-host mass ratio q2 = 0.9-1.2 × 10-5 = 3-4 ⊕ at 1σ, which is the lowest mass-ratio microlensing planet to date. Together with two other recent discoveries (4 ≲ q/q⊕ ≲ 6), it fills out the previous empty sector at the bottom of the triangular (log s, log q) diagram, where s is the planet-host separation in units of the angular Einstein radius θE. Hence, these discoveries call into question the existence, or at least the strength, of the break in the mass-ratio function that was previously suggested to account for the paucity of very low-q planets. Due to the extreme magnification of the event, Amax ~ 1450 for the underlying single-lens event, its light curve revealed a second companion with q3 ~ 0.05 and |log s3| ~ 1, i.e., a factor ~ 10 closer to or farther from the host in projection. The measurements of the microlens parallax πE and the angular Einstein radius θE allow estimates of the host, planet and second companion masses, (M1, M2, M3) ~ (0.3 M⊙, 1.0 M⊕, 17 MJ), the planet and second companion projected separations, (a⊥,2, a⊥,3) ~ (1.5, 0.15 or 15) au, and system distance DL ~ 1 kpc. The lens could account for most or all of the blended light (I ~ 19.3) and so can be studied immediately with high-resolution photometric and spectroscopic observations that can further clarify the nature of the system. The planet was found as part of a new program of high-cadence follow-up observations of high-magnification events. The detection of this planet, despite the considerable difficulties imposed by COVID-19 (two KMT sites and OGLE were shut down), illustrates the potential utility of this program.