Physically possible to slightly exceed mach 3.4 in the atmosphere, but there's no good use case now that we have spy satellites and ICBMs going through space at mach 19. Conventional ordnance will cook off at mach 3.4 due to drag.

Energy dissipation due to drag increases as the cube of speed, but blackbody radiation increases as the fourth power of temperature, so fuselage temperature should only increase as speed^0.75. SR-71 at top speed would have had a leading edge temperature of almost 500C, but you might be able to squeeze another 100C out of titanium alloys before you need a completely different material.

assuming the SR-71 had an aerodynamic cross-sectional-area of 17m^2, which is just a guess from eyeballing the schematics, and a drag coefficient at mach 3.4 of 0.25 from eyeballing another chart, I calculate the energy dissipation due to drag at top speed is around 100MW. Engines that powerful are not hard to build, but getting them to be that powerful and not melt at mach 3.4 and ~0.05kg/m^3 air density is the hard part. Also not melting the fuselage is hard when crusing above mach 3.5.