  We show that the metamagnetic transition in Sr$_4$Ru$_3$O$_{10}$ bifurcates
into two transitions as the field is rotated away from the conducting planes.
This two-step process comprises partial or total alignment of moments in
ferromagnetic bands followed by an itinerant metamagnetic transition whose
critical field increases with rotation. Evidence for itinerant metamagnetism is
provided by the Shubnikov-de Hass effect which shows a non-trivial evolution of
the geometry of the Fermi surface and an enhancement of the quasiparticles
effective-mass across the transition. The metamagnetic response of
Sr$_4$Ru$_3$O$_{10}$ is orbital-dependent and involves ferromagnetic and
metamagnetic bands.
