The bilayer ruthenate Sr3Ru2O7 has been cited as a textbook example of itinerant metamagnetic quantum criticality. However, recent studies of the ultrapure system have revealed striking anomalies in magnetism and transport in the vicinity of the quantum critical point. Drawing on fresh experimental data, we show that the complex phase behavior reported here can be fully accommodated within the framework of a simple Landau theory. We discuss the potential physical mechanisms that underpin the phenomenology, and assess the capacity of the ruthenate system to realize quantum tricritial behavior.