In select heterostructures comprising various atomically-thin van der Waals (vdW) materials, coupling to a moiré superlattice results in the emergence of flat electronic bands capable of hosting a wide array of correlated ground states. In twisted graphene heterostructures consisting of three or more total graphene sheets, the phase diagram can be tuned by a combination of the twist angle, charge doping, electric field, and pressure. I will discuss recent progress in probing and controlling correlated states in two different twisted graphene multilayer platforms. In twisted double bilayer graphene (tDBG) – two rotated sheets of Bernal-stacked bilayer graphene – spin-polarized correlated insulating states emerge at half filling of the conduction band. Neighboring correlated metallic states exhibit abrupt drops in the device resistivity as the temperature is lowered, providing additional signatures of spontaneous symmetry breaking. In heterostructures of twisted monolayer-bilayer graphene (tMBG), low crystal symmetry leads to different correlated ground states for opposite signs of an applied electric field, qualitatively resembling either tDBG or twisted bilayer graphene. Correlated topological states additionally emerge for certain twist angles, exhibiting ferromagnetism and a large associated anomalous Hall effect at low temperature. Uniquely, the magnetic order can be switched purely with electrostatic doping at zero magnetic field. Twisted multilayer graphene heterostructures therefore provide a platform for investigating and tuning correlated and topological states with an extraordinary degree of control.