Bilayer strontium ruthenate Sr 3 Ru 2 O 7 displays pronounced non-Fermi liquid behavior at magnetic fields around 8 T, applied perpendicular to the ruthenate planes, which previously has been associated with an itinerant metamagnetic quantum critical end point (QCEP). We focus on the magnetic Grüneisen parameter Γ H , which is the most direct probe to characterize field-induced quantum criticality. We confirm quantum critical scaling due to a putative two-dimensional QCEP near 7.845(5) T, which is masked by two ordered phases A and B, identified previously by neutron scattering. In addition we find evidence for a QCEP at 7.53(2) T and determine the quantum critical regimes of both instabilities and the effect of their superposition.Quantum criticality denotes critical behavior that is associated with continuous transformations of matter at zero temperature. Due to the absence of thermal fluctuations at T = 0 it is qualitatively different from classical criticality [1]. In metals the unconventional excitation spectrum near a quantum critical point (QCP) causes the breakdown of Fermi liquid (FL) behavior and its intimate relation to exotic states, such as unconventional superconductivity, adds even more importance to this topic. To date, the influence of quantum critical magnetic excitations on electrons in a metal is far from being understood. For instance the applicability of the itinerant Hertz-Millis-Moriya theory on f -electron based Kondo lattice systems has been disproved by several experiments [2] and alternative descriptions are not fully established yet. Quantum criticality related to itinerant metamagnetism is exceptional in the sense, that electronic degrees of freedom are irrelevant, and a quantitative application to experimental results should be possible [3].The generic metamagnetic quantum critical end point (QCEP) arises from the suppression to T = 0 of the end point of a line of first-order metamagnetic transitions in temperature-field phase space by tuning e.g. composition, pressure or the magnetic field orientation [3]. Metamagnetic QCEPs have been realized in the f -electron based compounds CeRu 2 Si 2 [4,5] We focus on bilayer strontium ruthenate Sr 3 Ru 2 O 7 . Magnetization of this compound along the tetragonal c-axis at low temperature exhibits three successive super-linear, i.e. metamagnetic, rises at µ 0 H M1 =7.5 T, µ 0 H M2 =7.85 T and µ 0 H M3 =8.1 T [9]. The first one is a metamagnetic cross-over (M1). The second and third ones are first order metamagnetic transitions (M2 and M3), ending at critical temperatures of about 1 and 0.5 K, respectively [10]. A line of second-order thermal phase transitions, connecting the critical end points of M2 and M3, has been discovered in electrical resistivity and thermodynamic experiments [10,11], which recently by neutron scattering has been identified as phase boundary of a spindensity-wave (SDW) "phase A" [12, 13] (see Fig. 1.). The lower and upper critical fields of SDW-A correspond respectively to H M2 and H M3 . Additionally, another SDW "ph...