We present AT2020mrf (SRGe J154754.2+443907), an extra-galactic ( z = 0.1353) fast blue optical transient (FBOT) with a rise time of t g,rise = 3.7 days and a peak luminosity of M g,peak = −20.0. Its optical spectrum around peak shows a broad ( v ∼ 0.1 c) emission feature on a blue continuum ( T ∼ 2 × 10 4 K), which bears a striking resemblance to AT2018cow. Its bright radio emission ( ν L ν = 1.2 × 10 39 erg s −1; ν rest = 7.4 GHz; 261 days) is similar to four other AT2018cow-like events, and can be explained by synchrotron radiation from the interaction between a sub-relativistic (≳0.07–0.08c) forward shock and a dense environment ( for v w = 10 3 km s −1). AT2020mrf occurs in a galaxy with M * ∼ 10 8 M ⊙ and specific star formation rate ∼10 −10 yr −1, supporting the idea that AT2018cow-like events are preferentially hosted by dwarf galaxies. The X-ray luminosity of AT2020mrf is the highest among FBOTs. At 35–37 days, SRG/eROSITA detected luminous ( L X ∼ 2 × 10 43 erg s −1; 0.3–10 keV) X-ray emission. The X-ray spectral shape ( f ν ∝ ν −0.8) and erratic intraday variability are reminiscent of AT2018cow, but the luminosity is a factor of ∼20 greater than AT2018cow. At 328 days, Chandra detected it at L X ∼ 10 42 erg s −1, which is >200 times more luminous than AT2018cow and CSS161010. At the same time, the X-ray emission remains variable on the timescale of ∼1 day. We show that a central engine, probably a millisecond magnetar or an accreting black hole, is required to power the explosion. We predict the rates at which events like AT2018cow and AT2020mrf will be detected by SRG and Einstein Probe.