The (ambi-)twistor model for spinning particles interacting via electromagnetic field is studied as a toy model for studying classical dynamics of gravitating bodies including effects of both spins to all orders. The all-orders-in-spin effects are encoded as a dynamical implementation of the Newman-Janis shift. It is found that the expansion in both spins can be resummed to simple expressions in special kinematic configurations, at least up to next-to-leading order. It is also observed that cutting rules associated with causality prescription for worldline propagators can be viewed as Poisson brackets of subdiagrams.