TmAgGe is an antiferromagnet based on the ZrNiAl structure. At low temperatures the spins are confined to distorted kagome-like planes, wherein the magnetisation is strongly anisotropic. A previous study has shown that a series of stepped magnetic transitions are apparent in low, in-plane magnetic fields and can be explained using a three-fold Ising-like model. Here we present high-magnetic-field magnetisation experiments showing that further stepped transitions are observed when the field is directed out of the kagome planes. Angledependent measurements in fields of up to 55 T show that there are at least two distinct and separate energy scales present in this system; the weak exchange interactions and the strong crystalline electric field interactions. Simulations of the magnetisation using a three-dimensional, free-energy minimisation technique allow us to suggest the nature and hierarchy of the forces acting on the Tm3+moments.