Motivated by the intriguing properties of the Shastry-Sutherland compound
SrCu2(BO3)2 under pressure, with a still debated intermediate plaquette phase
appearing at around 20 kbar and a possible deconfined critical point at higher
pressure upon entering the antiferromagnetic phase, we have investigated its
high-field properties in this pressure range using tunnel diode oscillator
(TDO) measurements. The two main new phases revealed by these measurements are
fully consistent with those identified by infinite Projected Entangled Pair
states (iPEPS) calculations of the Shastry-Sutherland model, a 1/5 plateau and
a 10 x 2 supersolid. Remarkably, these phases are descendants of the
full-plaquette phase, the prominent candidate for the intermediate phase of
SrCu2(BO3)2. The emerging picture for SrCu2(BO3)2 is shown to be that of a
system dominated by a tendency to an orthorhombic distortion at intermediate
pressure, an important constraint on any realistic description of the
transition into the antiferromagnetic phase