We predict the occurrence of unexpected magnetic ground states in ultrathin Mn films due to the frustration of higher-order interactions. Based on density functional theory we show that significant chiral-chiral interactions occur in hexagonal Mn monolayers due to large topological orbital moments which interact with the emergent magnetic field. Due to the competition with biquadratic and four-spin interactions superposition states of spin spirals such as the 2Q state or a distorted 3Q state arise. Simulations of spin-polarized scanning tunneling microscopy images suggest that the distorted 3Q state could be the magnetic ground state of a Mn monolayer on Re(0001).